The Clarets' hopes of another giant-killing and a place in the quarter-finals of the Carling Cup were cruelly dashed in extra time on a dramatic night at Villa Park.
Clarke Carlisle's last-gasp equaliser kept Burnley's Wembley dream flickering as they cancelled out Emile Heskey's 85th-minute opener and pushed the Premier League side to the brink.
But after Stuart Downing had rifled home five minutes into the extra half hour, ten-man Villa clung on to repel the Clarets' brave bid and limp into the last eight.
Marc Albrighton's dismissal for bundling over Wade Elliott as he bore down on goal left Villa a man down for the final 21 minutes.
The Clarets piled on the pressure but with Brad Friedel standing firm in the Villa goal, the second equaliser wouldn't come as last season's losing finalists sneaked through.
It was another titanic effort from the Clarets in a competition that has consistently brought out the best in them.
And despite the disappointment of defeat they showed the strength of a squad that boss Brian Laws will hope can now kick on in the Championship.
Laws had made six changes to the side that surrendered the Clarets' home record last Saturday with Lee Grant, Michael Duff, Clarke Carlisle, Graham Alexander, Ross Wallace and Martin Paterson all getting a chance to try and trigger an upset.
And the collective response prompted an up-tempo start as the Clarets zipped the ball around, with Paterson twice going close to getting onto the end of probing passes from Ross Wallace.
Burnley did their best to cramp Villa's style and make life difficult for the Premier League side, which started without a recognised out-and-out striker in a line-up which also saw six changes to their last top-flight outing.
But with Ashley Young playing in a forward role, the hosts were blessed with pace and whenever they looked to break they did so with menace.
Stephen Ireland offered support to Young and the pair combined for Ireland to get in a shot which Grant comfortably saved.
But the Clarets' keeper had to perform heroics to keep Burnley level mid-way through the first half.
Again Ireland and Young were involved as Villa advanced down their right. And when Young pulled the ball back, Nigel Reo-Coker looked a certain scorer until Grant made a fantastic double save.
Even then the danger wasn't averted but Grant again spread himself brilliantly to smother Barry Bannan's follow-up.
The Clarets' didn't help their cause at times by giving away possession in dangerous areas but some determined defending, with Duff impressing in only his third appearance of an injury-hit season, limited the potential damage as Villa's only other sight of goal before the break saw Young drag a shot tamely wide.
Laws made a subtle change at the start of the second half with Cork and Alexander swapping midfield roles as Alexander resumed his anchoring role.
And from that platform, Burnley sprung the Villa defence with Paterson firing over a cross which just eluded Jay Rodriguez at the far post.
Paterson was beginning to cause Villa problems and with 55 minutes gone he was only inches from giving Burnley the lead as the Premier League side was forced onto the back foot.
A quick free-kick from Alexander released Paterson and after turning inside Ciaran Clark, the Northern Ireland curled a low shot just wide of the target.
Villa boss Gerard Houllier responded by sending on Heskey but it was Burnley who continued to attack and this time it was an excellent double save from veteran keeper Friedel that kept the scoreline blank.
The former Blackburn keeper first palmed away a fierce shot on the turn from Paterson and then from Rodriguez's headed follow-up made an even better to stop to keep the ball out of the top corner.
Rodriguez and Paterson were proving a real handful and after Friedel had been forced to tip a Rodriguez header over the top, the young Claret collected the resulting corner and fired into the side netting as Burnley continued to force the pace.
With Villa struggling to regain the initiative, Houllier strengthened further with the introduction of Downing and the winger should have made the move pay with 18 minutes to go.
Downing had scored a quick-fire double when Villa beat Burnley here in the Premier League in February but this time his finishing was awry as he sliced an effort well wide when faced with just Grant to beat.
Heskey wasn't so wasteful when his chance came as the former England striker slid the ball home as the Clarets were undone on the break and Young crossed for Heskey to score from eight yards.
But the never-say-die spirit the Clarets showed in their heroic cup run two years ago surfaced again as Carlisle took the game into extra time.
The big defender was surrounded by three Villa players as he went up for a free-kick but when Wallace accepted Paterson's lay-off to clip a cross beyond the back post, Carlisle showed the strength to nod down and into the bottom corner of the net.
Carlisle heads home
An added half hour was the least the Clarets deserved - but five minutes in they were behind again as Downing found his range.
Burnley held up the initial attack but when Downing regained possession he was given space to lash a shot past Grant and into the top corner.
Having to do it all again, the Clarets, lifted by 3,000 travelling supporters, bravely picked themselves up and went on the attack again.
Steven Thompson slipped fellow substitute Elliott through for a run on goal and when he was pushed over just outside the box, Albrighton was sent off.
Wallace cracked the free-kick past the wall but Friedel made a fine save and when Tyrone Mears fired the loose ball back in, Eric Lichaj was lucky to get away without conceding a penalty as he blocked with his hand.
Friedel was becoming a central figure and the giant American then saved from Elliott as he latched onto a header down from Thompson to flick the ball goalwards.
And then with only seconds to go at the end of the second period of extra time Friedel made a superb save from Mears to break Burnley hearts as Chris Iwelumo's header from the rebound was cleared off the line by Carlos Cuellar in the last act of a thrilling cup tie.
Burnley: Grant, Mears, Fox, Carlisle, Duff, Alexander, Marney (Elliott 69), Cork (Thompson 88), Rodriguez, Paterson (Iwelumo 105), Wallace. Subs: Edgar, Bikey, Easton, Jensen.
Aston Villa: Friedel, Lichaj, Clark, Cuellar, Beye, Sidwell (Collins 118), Albrighton, Reo-Coker, Bannan (Downing 64), Young, Ireland (Heskey 59). Subs: Delfouneso, Hogg, Johnson.
Referee: Mike Jones.
Booked: Burnley: Marney 28
Villa: Reo-Coker 81
Sent off: Albrighton 99