Marathon man Jack Cork produced the goods again as the Clarets struck twice in extra time to reach the third qualifying round of the Europa League and set up a tie with Turkish side Istanbul Basaksehir.
Cork played every minute of last season - and ran further than anyone else - in the Premier League to help secure the seventh-place finish which brought European football back to Burnley for the first time in over 50 years.
And the midfielder was still going strong in extra time at the end of a gripping contest to head the goal that finally killed off Aberdeen’s unwilting challenge before Ashley Barnes kept his cool to convert a penalty four minutes from the end of a historic and – ultimately – glorious night at Turf Moor.
The second leg of the second-round qualifier had gone the full distance after Chris Wood’s early goal for the Clarets had been cancelled out by Aberdeen midfielder Lewis Ferguson’s spectacular strike just before the half hour.
And the two sides then refused to give an inch, going at it hammer and tongs in a full-blooded Anglo-Scottish tussle.
The Clarets had the better of the chances as Dons keeper Joe Lewis produced heroics.
But the Scots always carried a goal threat of their own to keep the tie on a knife edge until Burnley saved the best until last to seal a landmark victory.
The Clarets were given the perfect start as they went ahead in the tie for the first time with just five minutes gone.
Wood had scored twice for Birmingham in the group stages of the competition in 2011 and the striker opened his European account with a classy finish.
Ashley Westwood’s ball over the top was perfectly delivered but the striker still had plenty to do as he got there first ahead of Lewis.
Having held off the keeper, Wood kept his composure to turn and steer a powerful left-foot strike past two covering defenders into the roof of the net to reflect the Clarets’ early domination.
Aberdeen had barely been allowed out of their own half as Burnley dictated possession and pulled the visitors around.
But having recovered from that setback the Scots eased their way into the contest and fired a warning when Gary Mackay-Steven was left in space at the back post to let fly with a shot which was blocked by Stephen Ward.
And when Mackay-Steven then popped up on the opposite flank five minutes later he helped bring about the equaliser as Aberdeen grabbed the away goal to cancel out the one Sam Vokes had plundered late on at Pittodrie in the first leg to earn a starting slot in the only change to Burnley’s line-up.
Wood had come back to help out his defence but when his headed clearance from Mackay-Stevens’ cross dropped into the penalty area, teenager Ferguson pounced to send a superb overhead volley into the top corner.
The Clarets looked to respond as the tempo went up a gear, James Tarkowski flicking a header wide from a near-post Johann Berg Gudmundsson.
Wood then looked to be pulled back as he got away from Dons defender Scott McKenna to set up a run on goal.
But the visitors got the rub of the green on that decision and just before the break it took an excellent finger-tip save from Anders Lindegaard – making his full Burnley debut following injuries to Nick Pope and Tom Heaton – to prevent them going ahead as he touched away a low skidding drive from the impressive Graeme Shinnie.
Dyche sent on Barnes in place of injured goalscorer Wood at the start of the second half and the Clarets again took the early initiative with Lewis this time needing to produce a top-drawer save to keep the scores level.
Ben Mee’s ball forward was nodded down by Vokes for Gudmundsson to send a first-time strike towards the bottom corner which Lewis did well to push around a post.
Gudmundsson was suddenly causing the Dons’ defence all sorts of problems and teed up a chance for Barnes which the striker could not convert.
And for a spell the Clarets swarmed all over the former European Cup Winners’ Cup winners – who start their Scottish Premiership campaign against Glasgow Rangers on Sunday – as they looked to get their noses back in front.
But, as in the first half, Derek McInnes’ side, backed by a superb and noisy away following, hung in to stay very much in the contest, knowing that a goal for them on the break would leave the Clarets needing two to progress.
And with 25 minutes to go they nearly got it, Shinnie again picking up the ball in a dangerous area but this time lifting his effort over the bar from outside the penalty area.
In what was developing into a pulsating cup tie Burnley came back again and it took another piece of brilliant goalkeeping from Lewis to deny Barnes, who was superbly picked out by Cork to arrow in a shot which Lewis palmed over the top.
But Aberdeen weren’t just hanging on, Shinnie getting forward again to force Lindegaard into another save at his near post.
It was end-to-end stuff and with 15 minutes to go Lewis was Aberdeen’s saviour again, this time finger-tipping a Vokes header onto the underside of the bar when it looked like the striker had steered a perfect Matt Lowton cross into the roof of the net.
Nobody, from either side, was leaving anything out there but they had to go for another 30 minutes as the stalemate meant extra time.
The Clarets sent on fresh legs in the shape of Charlie Taylor, shortly after Dwight McNeil had been thrust onto the big stage, and within minutes he had whipped over a dangerous cross which Gudmundsson almost turned in at the near post – Andrew Considine making a vital block.
And it was Taylor who then provided the cross at the end of an excellent Burnley move for the Clarets to go back in front, Cork timing his run into the box perfectly to head a trademark goal and make it 2-1 on the night with 101 minutes on the clock.
Even then a second equaliser from Aberdeen would have taken them through on away goals.
But the Clarets did more than sit on their lead and with six minutes to go they finally made the game safe and booked a flight to Istanbul next week.
Gudmundsson was key again with a driving run into the box and when his cross was handled by Scott McKenna the Clarets had their first penalty since last August.
Thankfully Barnes hadn’t forgotten what to do as he sent the defiant Lewis the wrong way to set up phase two of the Clarets' European tour.
Burnley: Lindegaard, Lowton, Tarkowski, Mee, Ward (Taylor 90), Lennon (McNeil 86), Cork, Westwood (Hendrick 105), Gudmundsson, Vokes, Wood (Barnes HT). Substitutes: Legzdins, Bardsley, Long.
Booked: Gudmundsson, Lowton
Aberdeen: Lewis, Logan, McKenna, Devlin, Hoban (Ball 88), Considine, Shinnie, Ferguson (Chris Forrester 105), Mackay-Steven, Cosgrove (May 100), McGinn (Wright 81). Substitutes: Cerny, Forrester, Gleeson, May, Campbell.
Booked: Shinnie, Considine
Referee: Massimiliano Irrati (Italy)