Oldham boosted their hopes of staying in League One thanks to Deane Smalley's late winner against Bristol Rovers, whose play-off hopes have been dented.
The Latics took a deserved lead after half-time as Lewis Guy volleyed in from Paul Black's cross from the left.
Oldham's Joe Colbeck hit the outside of the post but Rovers levelled as Andy Williams set up Kuffour.
The Latics made sure of the points when Danny Whitaker crossed for substitute Smalley to head in at the far post.
Oldham boss Dave Penney told BBC Radio Manchester: "I don't think 46 (points) is enough to keep you up, so we'll go to MK and try and get another three points.
"I've never set a target where I wanted to finish or a points target and I won't do now, just keep going until the next game and try and pick up as many points as we can.
"We've give Deane a bit of a reality check, left him out for a couple of games and that's the way you react."
Bristol Rovers manager Paul Trollope told BBC Radio Bristol:
"I thought we dominated the first half, passed it well and pushed them back down the hill, creating a few half chances and a lot of pressure.
"But when you've got that domination in a game you need to score, and we didn't get that breakthrough.
"Obviously they got a lift from a poor bit of defending by us for the goal, which took the wind out of our sails for a little bit."
90:00+3:24 The game is over, as the referee blows his whistle.
90:00+2:06 Effort on goal by Lewis Guy from inside the penalty box misses to the right of the target.
90:00+1:25 Free kick awarded for a foul by Danny Coles on Alex Marrow. Dale Stephens takes the direct free kick.
90:00+0:46 Free kick awarded for a foul by Tom Eaves on Danny Coles. Free kick taken by Mikkel Andersen.
90:00+0:06 Jo Kuffour takes a shot. Darryl Flahavan makes a fantastic save.
89:26 The ball is sent over by Daniel Jones, Sean Gregan makes a clearance.
88:04 Substitution Dean Furman is brought on as a substitute for Pawel Abbott.
87:24 Assist on the goal came from Danny Whitaker.
87:24 GOAL - Deane Smalley:Oldham 2 - 1 Bristol Rovers Deane Smalley scores a headed goal from close range. Oldham 2-1 Bristol Rovers.
87:19 The ball is crossed by Danny Whitaker,
86:35 Indirect free kick taken by Dale Stephens.
86:35 Booking Danny Coles receives a yellow card for unsporting behaviour.
86:21 Danny Coles challenges Danny Whitaker unfairly and gives away a free kick.
86:02 Daniel Jones crosses the ball.
85:39 The ball is swung over by Dale Stephens.
85:24 Alex Marrow crosses the ball, clearance made by Danny Coles.
84:44 The ball is swung over by Alex Marrow, Headed effort from inside the area by Tom Eaves misses to the right of the goal.
83:51 Shot from just outside the box by Pawel Abbott goes over the bar.
83:28 Free kick awarded for a foul by Chris Lines on Lewis Guy. Alex Marrow takes the indirect free kick.
82:35 Shot from long range by Danny Whitaker goes wide of the left-hand upright.
82:17 Byron Anthony gives away a free kick for an unfair challenge on Lewis Guy. Dale Stephens takes the indirect free kick.
81:29 Andrew Williams fouled by Deane Smalley, the ref awards a free kick. Stuart Campbell crosses the ball from the free kick right-footed from right wing, Sean Gregan makes a clearance.
80:39 Stuart Campbell takes a outswinging corner to the near post, clearance by Deane Smalley.
79:50 Outswinging corner taken left-footed by Ben Swallow from the left by-line.
79:43 The ball is sent over by Jo Kuffour, Sean Gregan makes a clearance.
78:41 Free kick awarded for an unfair challenge on Stuart Campbell by Deane Smalley. Mikkel Andersen takes the indirect free kick.
77:45 Unfair challenge on Byron Anthony by Pawel Abbott results in a free kick. Byron Anthony takes the indirect free kick.
76:45 Andrew Williams provided the assist for the goal.
76:45 GOAL - Jo Kuffour:Oldham 1 - 1 Bristol Rovers Jo Kuffour finds the back of the net with a goal from close in to the bottom right corner of the goal. Oldham 1-1 Bristol Rovers.
76:41 Centre by Andrew Williams,
76:06 Free kick awarded for a foul by Danny Whitaker on Stuart Campbell. Mikkel Andersen takes the free kick.
75:31 Substitution Tom Eaves comes on in place of Joe Colbeck.
75:00 Daniel Jones sends in a cross, free kick awarded for an unfair challenge on Sean Gregan by Chris Lines. Free kick taken by Darryl Flahavan.
74:06 Pawel Abbott takes a shot. Danny Coles gets a block in.
70:04 Daniel Jones concedes a free kick for a foul on Deane Smalley. Darryl Flahavan restarts play with the free kick.
68:34 Inswinging corner taken right-footed by Dale Stephens played to the near post, Byron Anthony makes a clearance.
68:25 Dale Stephens takes a shot. Blocked by Danny Coles.
66:12 Sean Gregan gives away a free kick for an unfair challenge on Jo Kuffour. Strike comes in from Chris Lines from the free kick, blocked by Lewis Guy.
Correction - 65:14 Substitution (Bristol Rovers) makes a substitution, with Ben Swallow coming on for Dominic Blizzard.
Correction - 65:14 Foul by Paul Black on Stuart Campbell, free kick awarded.
65:14 Mikkel Andersen restarts play with the free kick.
65:14 Substitution Ben Swallow on for Dominic Blizzard.
65:14 Paul Black concedes a free kick for a foul on Stuart Campbell.
62:14 Corner taken right-footed by Stuart Campbell from the left by-line, save made by Darryl Flahavan.
61:26 Corner from the right by-line taken by Stuart Campbell, Danny Coles takes a shot. Paul Black gets a block in.
60:47 Deane Smalley concedes a free kick for a foul on Daniel Jones. Mikkel Andersen takes the free kick.
59:54 Joe Colbeck has an effort at goal from just outside the penalty box that bounces off the post.
58:37 Corner taken by Dale Stephens, The ball is crossed by Joe Colbeck, save by Mikkel Andersen.
58:31 The ball is sent over by Deane Smalley, blocked by Daniel Jones.
56:45 Unfair challenge on Lewis Guy by Steve Elliott results in a free kick. A cross is delivered by Dale Stephens, Headed effort from deep inside the area by Pawel Abbott misses to the left of the goal.
55:10 Stuart Campbell takes a inswinging corner from the left by-line to the near post, Deane Smalley makes a clearance.
54:18 Paul Black sends in a cross, Pawel Abbott has shot on goal from just outside the box which goes wide of the right-hand upright.
53:37 The official flags Jeff Hughes offside. Indirect free kick taken by Darryl Flahavan.
52:27 Free kick taken by Steve Elliott.
52:27 Substitution (Bristol Rovers) makes a substitution, with Andrew Williams coming on for Darryl Duffy.
52:27 Free kick awarded for an unfair challenge on Daniel Jones by Danny Whitaker.
51:36 Unfair challenge on Chris Lines by Dale Stephens results in a free kick. Mikkel Andersen restarts play with the free kick.
50:15 The assistant referee flags for offside against Darryl Duffy. Free kick taken by Darryl Flahavan.
49:11 Pawel Abbott takes a shot. Save by Mikkel Andersen.
47:17 Paul Black provided the assist for the goal.
47:17 GOAL - Lewis Guy:Oldham 1 - 0 Bristol Rovers Lewis Guy grabs a goal from inside the six-yard box to the top left corner of the goal. Oldham 1-0 Bristol Rovers.
47:13 Paul Black sends in a cross,
45:01 The second half begins.
45:01 Substitution (Oldham) makes a substitution, with Deane Smalley coming on for Chris Taylor.
Half Time
45:00+2:29 The half-time whistle blows.
45:00+2:02 The referee blows for offside against Sean Gregan.
45:00+1:23 Indirect free kick taken by Dale Stephens.
45:00+1:23 Booking The referee cautions Steve Elliott for unsporting behaviour.
45:00+1:18 Steve Elliott concedes a free kick for a foul on Joe Colbeck.
44:04 Free kick awarded for an unfair challenge on Reuben Hazell by Darryl Duffy. Alex Marrow takes the free kick.
41:59 Reuben Hazell challenges Jo Kuffour unfairly and gives away a free kick. Chris Lines has a direct shot on goal from the free kick.
39:00 Chris Taylor gives away a free kick for an unfair challenge on Dominic Blizzard. Free kick taken by Mikkel Andersen.
38:44 Foul by Dominic Blizzard on Dale Stephens, free kick awarded. Indirect free kick taken by Reuben Hazell.
38:20 Darryl Duffy is flagged offside by the assistant referee. Reuben Hazell restarts play with the free kick.
36:00 Joe Colbeck gives away a free kick for an unfair challenge on Daniel Jones. Direct free kick taken by Steve Elliott.
33:46 The referee blows for offside. Darryl Flahavan restarts play with the free kick.
33:08 Corner taken by Stuart Campbell from the left by-line played to the near post, Pawel Abbott manages to make a clearance.
32:10 Reuben Hazell gives away a free kick for an unfair challenge on Jo Kuffour. Shot comes in from Chris Lines from the free kick, Darryl Flahavan makes a save.
30:46 The referee blows for offside. Indirect free kick taken by Mikkel Andersen.
30:39 The ball is delivered by Joe Colbeck.
29:58 Danny Whitaker gives away a free kick for an unfair challenge on Stuart Campbell. The free kick is swung in right-footed by Stuart Campbell, save by Darryl Flahavan.
29:03 The referee gives a free kick against Pawel Abbott for handball. Mikkel Andersen takes the free kick.
28:03 A cross is delivered by Byron Anthony.
26:18 Outswinging corner taken by Dale Stephens.
26:05 Pawel Abbott takes a shot. Save by Mikkel Andersen.
25:35 Unfair challenge on Sean Gregan by Darryl Duffy results in a free kick. Free kick taken by Sean Gregan.
23:38 Darryl Duffy delivers the ball.
22:04 Corner from the left by-line taken by Stuart Campbell, clearance made by Alex Marrow.
21:13 Corner crossed in by Stuart Campbell, clearance by Sean Gregan.
19:36 Effort on goal by Jo Kuffour from just outside the area goes harmlessly over the target.
Correction - 17:33 Lewis Guy challenges Danny Coles unfairly and gives away a free kick. Free kick taken by Stuart Campbell. Header from close in by Jo Kuffour misses to the left of the goal.
17:33 Lewis Guy gives away a free kick for an unfair challenge on Danny Coles. Free kick taken by Stuart Campbell. Jo Kuffour produces a header from close range which goes wide of the left-hand upright.
15:12 Stuart Campbell fouled by Dale Stephens, the ref awards a free kick. Chris Lines restarts play with the free kick.
13:56 Joe Colbeck has shot on goal from just outside the penalty box which goes wide of the right-hand upright.
13:37 The ball is crossed by Pawel Abbott.
12:31 Centre by Paul Black, Danny Coles makes a clearance.
11:44 Effort on goal by Chris Lines from outside the penalty box goes harmlessly over the bar.
10:53 Free kick awarded for a foul by Joe Colbeck on Daniel Jones. Jeff Hughes takes the indirect free kick.
8:44 Danny Whitaker takes the indirect free kick. Dale Stephens takes a shot. Save by Mikkel Andersen.
8:44 Booking Caution for Chris Lines.
8:31 Chris Taylor fouled by Chris Lines, the ref awards a free kick.
5:44 Free kick awarded for an unfair challenge on Lewis Guy by Danny Coles. Dale Stephens takes the free kick.
5:23 Centre by Joe Colbeck, save by Mikkel Andersen.
3:10 Free kick awarded for an unfair challenge on Sean Gregan by Darryl Duffy. Free kick taken by Darryl Flahavan.
2:15 Outswinging corner taken right-footed by Stuart Campbell played to the near post, Pawel Abbott manages to make a clearance.
1:49 Outswinging corner taken right-footed by Stuart Campbell played to the near post, Sean Gregan makes a clearance.
1:26 Corner taken by Stuart Campbell from the right by-line to the near post, Reuben Hazell manages to make a clearance.
1:06 Jo Kuffour takes a shot. Reuben Hazell gets a block in.
0:00 The game begins.
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