By Dan Harrison
Super subs Emile Heskey and Stewart Downing sent Villa roaring into the quarter-finals as Villa Park witnessed another Carling Cup epic.
Just as he did in round three against Blackburn Rovers, Heskey came off the bench to make his mark on this clash late in normal time.
Clarke Carlisle's header with seconds remaining took the game into extra-time, before Downing produced a strike worthy of winning any cup tie.
However, there was added drama in the extra 30 minutes as Marc Albrighton saw red for bringing down Wade Elliott - ruling the 20-year-old out of Sunday's Second City derby against Birmingham City.
Villa made six changes from the weekend defeat at Sunderland, while Nigel Reo-Coker took over the captaincy for the first time in Stiliyan Petrov's absence.
The new stand-in skipper emerged for this fourth round tie intent on setting the standard.
Reo-Coker has been reborn since the arrival of Gerard Houllier and from the first whistle he seemed determined to maitainhis impressive run of all-action performances under the new gaffer.
The only thing lacking from the former England U21s captain was a finish.
He found himself at the start and end points of Villa's best move of the first period.
It was Reo-Coker's pass that Stephen Ireland controlled just inside the Burnley half and threaded neatly through to Ashley Young.
Young - operating as a striker after John Carew's late withdrawal through illness - cut back in to Reo-Coker's path but Lee Grant blocked his close range effort.
The rebound fell to Barry Bannan who was also denied by the quick reflexes of Burnley's keeper.
That, along with a half-chance for Ireland on 16 minutes, demonstrated the home side's patient build-ups followed by quick breaks from the middle of the park.
Ireland's half-volley forced Grant into action after some neat improvisation from Young to send the Irish midfielder racing towards goal.
But if the Clarets struggled to come up with any response to Villa's first-half dominance, Brian Laws' team emerged all guns blazing after the break.
Strike duo Martin Paterson and Jay Rodriguez plotted a revival for the visitors - the former forcing a stunning double save from Brad Friedel.
First, the American had to be at full stretch to parry Paterson's curling left-foot strike, before getting straight up to save the headed follow-up from Rodriguez.
There were further left-offs for Villa when Paterson gathered possession on the right-hand corner of the penalty area, moved inside past Ciaran Clark and shot just beyond the far post, while Rodriguez found the side netting from close range.
It prompted Houllier to turn to Heskey and Downing to conjure up some goalscoring magic.
Downing was quick to make his presence felt. Soon after replacing Barry Bannan, he beat the offside trap but guided his lofted left-foot effort off target.
The missed opportunity added to the hosts' frustration in front of goal after a Sidwell had missed Eric Lichaj's right-wing cross by inches earlier in the half.
But, after what was at times a subdued affair, the drama was saved until the death.
Heskey, the star turn in the previous round, thought he'd had the final say in this tie too when he met Young's centre to slot past Grant with five minutes remaining.
However, Carlisle had other ideas. This time Ross Wallace provided Burnley's creative spark, producing a delicate chipped cross for his team-mate to head home at the back post.
Carlisle's strike ensured an extra 30 minutes were required - and ignited even further drama in an already compelling contest.
Six minutes into the first period of extra-time, Downing made a run across the box and unleashed a powerful drive into the top corner which Grant couldn't keep out.
Villa had their noses in front again although the tie was far from over.
Substitute Elliott beat the offside trap and ran through on goal before being brought down from behind by Albrighton, resulting in a red card for the Tamworth-born winger.
It took a couple more crucial saves from Friedel to see Villa through.
The veteran stopper thwarted Elliott. Then, at the death he parried a powerful strike from Tyron Mears before the follow-up effort was headed off the line by Carlos Cuellar.
The draw for the Carling Cup quarter-final draw takes place on Saturday at 12.20pm.
VILLA: Friedel; Beye, Clark, Cuellar, Lichaj; Albrighton, Reo-Coker, Sidwell, Bannan; Ireland; A Young. Subs: Guzan, Downing (for Bannan, 63), Delfouneso, Heskey (for Ireland, 58), Hogg, Collins (for Sidwell, 116), Johnson.
BURNLEY: Grant, Alexander, Fox, Duff, Carlisle, Cork, Marney, Paterson, Mears, Rodriguez, Wallace. Subs: Jensen, Iwelumo (for Paterson, 105), Elliott (for Marney, 69), Edgar, Bikey, Easton, Thompson (for Cork, 87).