Ward should have finally broken the deadlock shortly after but, having been sent clear by Sheehan, the on-loan Bolton forward could only fire across the face of goal and wide.
After the break, Bailey curled a delightful effort towards the top corner that rebounded away off the inside of a post.
Three minutes later Swindon - and Austin - finally got the goal they deserved.
The frontman peeled off his marker with ease to plant Sheehan's left-wing cross past a helpless Randolph.
Ward doubled the the lead when he shot low past Randolph after Simon Ferry had taken advantage of a quick break and a two-on-one situation.
Burton reduced Charlton's arrears soon after, bravely heading home Randolph's long ball forward as keeper David Lucas came but failed to collect.
And the Addicks number 10 somehow failed to head level from a matter of yards just a few minutes later.
That miss could have proved extremely costly when Pericard was presented with a headed chance to restore Swindon's two-goal cushion but he directed his effort against the foot of the post.
Charlton manager Phil Parkinson told BBC London 94.9: "In the first half I thought Swindon settled more quickly than we did.
"At the start of the second half I thought we started very, very well, we really had a go at Swindon.
"To find ourselves 2-0 down was a disappointment because defensively we could have done better on the goals.
"The tables will be turned on Monday at The Valley, we're going to have a full house and a terrific crowd behind us."
90:00+5:01 The referee brings the game to a close.
90:00+4:25 Header from close in by Vincent Pericard bounces off the post.
90:00+2:10 Inswinging corner taken by Alan Sheehan.
90:00+1:20 Vincent Pericard gives away a free kick for an unfair challenge on Christian Dailly. Direct free kick taken by Darren Randolph.
90:00+0:32 Christian Dailly challenges Vincent Pericard unfairly and gives away a free kick. Scott Cuthbert restarts play with the free kick.
90:00+0:08 Daniel Ward has a headed effort at goal from close in which goes wide right of the target.
88:42 Substitution Vincent Pericard comes on in place of Charlie Austin.
87:02 Gary Borrowdale restarts play with the free kick.
87:02 Booking Jon-Paul McGovern receives a caution.
86:48 Free kick awarded for a foul by Jon-Paul McGovern on Nicky Bailey.
85:14 Free kick awarded for a foul by Daniel Ward on Sam Sodje. Direct free kick taken by Darren Randolph.
84:29 Nicky Forster is penalised for a handball. Direct free kick taken by Scott Cuthbert.
84:03 Shot from 35 yards by Nicky Forster went harmlessly over the net.
83:35 Substitution Michael Timlin is brought on as a substitute for Alan O'Brien.
83:13 Substitution Deon Burton goes off and Akpo Sodje comes on.
82:59 Daniel Ward produces a left-footed shot from the edge of the box and misses to the left of the target.
81:23 Daniel Ward takes a shot. Sam Sodje gets a block in.
78:29 Substitution Lloyd Sam goes off and Scott Wagstaff comes on.
78:09 Charlie Austin produces a header from deep inside the six-yard box that clears the bar.
76:15 Substitution Stephen Darby comes on in place of Kevin Amankwaah.
75:25 Corner taken by Gary Borrowdale from the right by-line played to the near post, David Lucas makes a save.
74:37 Corner taken left-footed by Gary Borrowdale to the near post, clearance by Gordon Greer.
73:18 Inswinging corner taken by Gary Borrowdale from the right by-line played to the near post, save by David Lucas.
72:59 Substitution (Charlton) makes a substitution, with Nicky Forster coming on for David Mooney.
70:59 Daniel Ward has an effort at goal from just outside the box which goes wide of the left-hand post.
70:41 Nicky Bailey sends in a cross.
68:46 Jose Vitor Semedo gives away a free kick for an unfair challenge on Jonathan Douglas. David Lucas takes the direct free kick.
68:18 Alan Sheehan challenges Lloyd Sam unfairly and gives away a free kick. Darren Randolph takes the free kick.
65:52 Frazer Richardson takes the inswinging corner, David Lucas fouled by Deon Burton, the ref awards a free kick. David Lucas restarts play with the free kick.
64:26 Assist on the goal came from Darren Randolph.
64:26 GOAL - Deon Burton:Swindon 2 - 1 Charlton Deon Burton scores a headed goal from inside the penalty area. Swindon 2-1 Charlton.
63:54 Centre by Alan O'Brien, save by Darren Randolph.
62:42 Corner from the right by-line taken by Alan Sheehan, Lloyd Sam makes a clearance.
62:32 A cross is delivered by Alan O'Brien, clearance by Gary Borrowdale.
61:54 The official flags Deon Burton offside. David Lucas takes the free kick.
59:27 The assist for the goal came from Simon Ferry.
59:27 GOAL - Daniel Ward:Swindon 2 - 0 Charlton Daniel Ward finds the net with a goal from deep inside the penalty box to the bottom right corner of the goal. Swindon 2-0 Charlton.
58:42 Gary Borrowdale takes the inswinging corner, clearance made by Gordon Greer.
56:05 Inswinging corner taken by Frazer Richardson from the left by-line played to the near post, Gordon Greer makes a clearance.
55:39 Inswinging corner taken by Gary Borrowdale, save by David Lucas.
54:51 Corner taken by Gary Borrowdale from the right by-line to the near post, clearance made by Jonathan Douglas.
54:21 Gary Borrowdale takes the inswinging corner, Jonathan Douglas manages to make a clearance.
53:38 Free kick awarded for an unfair challenge on David Mooney by Simon Ferry. Free kick crossed right-footed by Frazer Richardson from left channel, Gordon Greer makes a clearance.
52:03 David Mooney fouled by Gordon Greer, the ref awards a free kick. Gary Borrowdale has a direct shot on goal from the free kick.
51:01 The assist for the goal came from Alan Sheehan.
51:01 GOAL - Charlie Austin:Swindon 1 - 0 Charlton Charlie Austin scores a headed goal from inside the six-yard box. Swindon 1-0 Charlton.
50:58 Centre by Alan Sheehan,
50:06 Alan O'Brien gives away a free kick for an unfair challenge on Jose Vitor Semedo. Nicky Bailey takes the direct free kick.
48:38 Frazer Richardson takes the inswinging corner, clearance by Kevin Amankwaah.
48:25 Nicky Bailey has an effort at goal from just outside the penalty box hitting the post.
45:54 Gary Borrowdale takes a shot. Save by David Lucas.
45:01 The second half begins.
Half Time
45:00+2:07 The first half comes to an end.
45:00+2:00 The ball is sent over by Nicky Bailey.
43:19 Outswinging corner taken from the right by-line by Jon-Paul McGovern, clearance by Christian Dailly.
42:07 Free kick awarded for an unfair challenge on Gordon Greer by Therry Racon. Direct free kick taken by Alan Sheehan.
38:15 Corner taken right-footed by Frazer Richardson from the left by-line, clearance by Gordon Greer.
Correction - 37:54 Jose Vitor Semedo takes a shot. Jon-Paul McGovern gets a block in.
37:54 Effort on goal by Jose Vitor Semedo from outside the penalty box goes harmlessly over the bar.
37:18 Unfair challenge on Lloyd Sam by Alan Sheehan results in a free kick. Gary Borrowdale delivers the ball from the free kick left-footed from right by-line, save by David Lucas.
36:15 Free kick awarded for a foul by Simon Ferry on Jose Vitor Semedo. Free kick taken by Darren Randolph.
35:16 Lloyd Sam challenges Alan Sheehan unfairly and gives away a free kick. David Lucas restarts play with the free kick.
34:04 Nicky Bailey crosses the ball.
33:12 Centre by Frazer Richardson, save by David Lucas.
31:58 Jose Vitor Semedo gives away a free kick for an unfair challenge on Jonathan Douglas. Jon-Paul McGovern takes the direct free kick.
31:05 Daniel Ward produces a left-footed shot from deep inside the penalty area which goes wide of the right-hand post.
30:00 The referee penalises David Mooney for handball. Free kick crossed by David Lucas.
28:17 Close range headed effort by Jonathan Douglas misses to the right of the goal.
24:59 Unfair challenge on Alan Sheehan by David Mooney results in a free kick. Direct free kick taken by Alan Sheehan.
23:36 The official flags Charlie Austin offside. Darren Randolph restarts play with the free kick.
22:07 Alan Sheehan gives away a free kick for an unfair challenge on Lloyd Sam. Gary Borrowdale delivers the ball from the free kick left-footed from right by-line, clearance made by Gordon Greer.
20:06 Unfair challenge on Deon Burton by Gordon Greer results in a free kick. Free kick crossed left-footed by Gary Borrowdale, Gordon Greer manages to make a clearance.
19:28 Daniel Ward fouled by Christian Dailly, the ref awards a free kick. Gordon Greer takes the direct free kick.
18:21 Corner from right by-line taken by Jon-Paul McGovern.
18:06 Alan O'Brien takes a shot. Darren Randolph makes a save.
17:23 David Mooney gives away a free kick for an unfair challenge on Gordon Greer. Free kick taken by Alan Sheehan.
16:24 The assistant referee signals for offside against Deon Burton. David Lucas takes the free kick.
15:34 Shot from just outside the box by Nicky Bailey misses to the right of the goal.
14:25 Inswinging corner taken left-footed by Gary Borrowdale from the right by-line, save made by David Lucas.
13:54 The referee gives a free kick against Charlie Austin for handball. Direct free kick taken by Darren Randolph.
11:59 Free kick awarded for an unfair challenge on Deon Burton by Gordon Greer. Free kick crossed right-footed by Frazer Richardson, Scott Cuthbert manages to make a clearance.
11:21 Short corner worked by Jon-Paul McGovern.
Correction - 10:38 Christian Dailly challenges Daniel Ward unfairly and gives away a free kick. Alan Sheehan produces a cross, Charlie Austin takes a shot. Save by Darren Randolph.
10:38 Christian Dailly gives away a free kick for an unfair challenge on Daniel Ward. Alan Sheehan delivers the ball, Charlie Austin takes a shot. Save by Darren Randolph.
8:55 Charlie Austin takes a shot. Save by Darren Randolph.
5:42 Shot from 35 yards by Gary Borrowdale went harmlessly over the crossbar.
5:07 Outswinging corner taken from the right by-line by Frazer Richardson.
2:00 Daniel Ward has a headed effort at goal from close in which goes wide left of the target.
1:42 Charlie Austin takes a shot. Save by Darren Randolph.
1:18 Daniel Ward fouled by Jose Vitor Semedo, the ref awards a free kick. Alan Sheehan takes the free kick.
0:40 Foul by Charlie Austin on Sam Sodje, free kick awarded. Free kick taken by Darren Randolph.
0:00 The match gets underway.
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Swindon 2-1 Charlton
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