Winger Hogan Ephraim played a starring role as Leeds booked a Johnstone's Paint Trophy Northern Area final against Carlisle.
Ephraim, on loan from QPR, fired much-changed Leeds ahead in the ninth minute with a 20-yard shot from the left which deflected off defender Phil Edwards.
And Ephraim's 50th-minute run and cross from the right enabled Neil Kilkenny to head Leeds' second goal.
Accrington's best chance came when John Miles's deflected shot hit the post.
Leeds United manager Simon Grayson told BBC Radio Leeds:
"It was an average performance, but we've won the game and are through to the next round.
"Over the course of the game Accrington had the better chances and were the better team and I'm not sure how we kept a clean sheet.
"We know we need to be better than that when we take on Southampton at the weekend because they will punish you.
"We have to be a lot more dogged and determined and ruthless over the next few weeks if we are to be successful."
90:00+3:09 The referee blows his whistle to end the game.
90:00+1:51 Free kick awarded for an unfair challenge on Robert Grant by Jason Crowe. Direct free kick taken by Dean Bouzanis.
90:00+0:10 Corner from the left by-line taken by Luke Joyce, David Martin makes a save.
89:09 Foul by Lubomir Michalik on Sean McConville, free kick awarded. Shot on goal comes in from Robert Grant from the free kick, save made by David Martin.
81:51 Effort on goal by Sean McConville from inside the area goes harmlessly over the bar.
80:50 Unfair challenge on James Ryan by Lubomir Michalik results in a free kick. Dean Bouzanis takes the direct free kick.
80:24 Corner taken by Max Gradel.
79:52 Max Gradel takes a shot. Save by Dean Bouzanis.
77:50 The referee blows for offside. Free kick taken by Dean Bouzanis.
77:08 Unfair challenge on Jason Crowe by Robert Grant results in a free kick. Direct free kick taken by David Martin.
76:20 Substitution Patrick Kisnorbo is brought on as a substitute for Robert Snodgrass.
74:49 The referee penalises Robert Grant for handball. Max Gradel takes the direct free kick.
73:44 Corner taken right-footed by Luke Joyce, Hogan Ephraim manages to make a clearance.
69:20 Corner taken by Luke Joyce from the left by-line to the near post, Jason Crowe makes a clearance.
69:00 Shot by Robert Grant from deep inside the area bounces off the post.
68:02 The referee blows for offside against Robert Snodgrass. Dean Bouzanis takes the free kick.
67:15 Corner taken right-footed by Hogan Ephraim.
65:39 Sean McConville has an effort at goal from deep inside the area missing to the left of the goal.
64:56 John Miles produces a volleyed right-footed shot from just inside the penalty area and hits the post.
63:13 Substitution John Miles joins the action as a substitute, replacing Peter Murphy.
59:30 Free kick taken by David Martin.
59:30 Substitution Max Gradel is brought on as a substitute for Tresor Kandol.
59:30 Substitution Sam Vokes joins the action as a substitute, replacing Mike Grella.
59:30 Michael Symes gives away a free kick for an unfair challenge on Richard Naylor.
57:25 Michael Symes produces a right-footed shot from deep inside the penalty area which goes wide of the right-hand post.
56:49 Jason Crowe gives away a free kick for an unfair challenge on Andrew Procter. Free kick taken by Phil Edwards.
55:23 Free kick awarded for a foul by Phil Edwards on Mike Grella. Free kick taken by David Prutton.
54:28 Phil Edwards gives away a free kick for an unfair challenge on Tresor Kandol. Free kick taken by Neil Kilkenny.
53:12 Substitution Sean McConville on for Billy Kee.
53:01 The ball is swung over by Luke Joyce.
51:32 Andrew Procter gives away a free kick for an unfair challenge on Neil Kilkenny. Neil Kilkenny takes the free kick.
50:29 Unfair challenge on Michael Symes by David Prutton results in a free kick. Free kick taken by Dean Winnard.
49:27 Assist by Hogan Ephraim.
49:27 GOAL - Neil Kilkenny:Leeds United 2 - 0 Accrington Stanley Neil Kilkenny finds the back of the net with a headed goal from inside the penalty area. Leeds 2-0 Accrington Stanley.
48:27 Shot by Jason Crowe from outside the box goes over the target.
47:21 The referee penalises Michael Symes for handball. Free kick taken by David Martin.
46:12 A cross is delivered by Robert Snodgrass, save by Dean Bouzanis.
45:41 The ball is swung over by James Ryan, save made by David Martin.
45:01 The second half kicks off.
Half Time
45:00+1:00 The first half comes to an end.
43:47 Effort from outside the penalty area by Michael Symes goes wide left of the target.
39:06 Effort on goal by Andrew Procter from just inside the penalty box goes harmlessly over the target.
37:20 Effort from outside the penalty box by Robert Snodgrass goes wide right of the goal.
35:51 Corner taken right-footed by Luke Joyce, Michael Symes takes a shot. Save by David Martin.
33:50 The official flags Michael Symes offside. David Martin takes the direct free kick.
32:57 Corner taken by Robert Snodgrass, Dean Bouzanis makes a save.
32:46 Robert Snodgrass crosses the ball, clearance by Dean Winnard.
29:40 Hogan Ephraim takes a inswinging corner.
29:24 Tresor Kandol takes a shot. Save made by Dean Bouzanis.
28:46 Effort from 35 yards by Lubomir Michalik went wide right of the target.
28:34 The ball is delivered by Hogan Ephraim, James Ryan makes a clearance.
25:19 Darran Kempson concedes a free kick for a foul on Tresor Kandol. Jason Crowe takes the free kick.
21:43 Corner taken left-footed by Robert Snodgrass, Headed effort from inside the area by Tresor Kandol misses to the left of the goal.
20:51 The referee penalises Andy Hughes for handball. Direct free kick taken by Peter Murphy.
18:57 Free kick awarded for an unfair challenge on Andy Hughes by Andrew Procter. Free kick taken by David Martin.
18:23 Foul by Richard Naylor on Michael Symes, free kick awarded. Direct free kick taken by Dean Winnard.
17:44 The ball is swung over by Jason Crowe, Peter Murphy manages to make a clearance.
16:48 Mike Grella is flagged offside by the assistant referee. Dean Bouzanis takes the free kick.
15:00 A cross is delivered by Peter Murphy, clearance made by Jason Crowe.
11:59 The ball is crossed by Luke Joyce, Jason Crowe manages to make a clearance.
10:12 Corner from the left by-line taken by Luke Joyce, Richard Naylor makes a clearance.
8:23 GOAL - Hogan Ephraim:Leeds United 1 - 0 Accrington Stanley Hogan Ephraim finds the back of the net with a goal from long range to the bottom right corner of the goal. Leeds 1-0 Accrington Stanley.
7:05 Free kick awarded for a foul by Jason Crowe on Robert Grant. Dean Winnard restarts play with the free kick.
6:04 Corner from the left by-line taken by Hogan Ephraim, Darran Kempson makes a clearance.
2:21 James Ryan takes a shot. David Martin makes a save.
0:12 Inswinging corner taken left-footed by Robert Grant from the right by-line, Shot from 18 yards from Phil Edwards. Save made by David Martin.
0:00 The game kicks-off.
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