Super-sub Sam Vokes scored the Clarets’ first European goal in more than half a century to enhance hopes of extending the long-awaited return to Continental competition.
A controversial penalty, slotted past substitute goalkeeper Anders Lindegaard by Gary Mackay-Stevens, had threatened to make it a highly demanding second leg of this Europa League second qualifying round at Turf Moor in a week’s time.
And Sean Dyche’s men still have plenty of work to do to make sure they are the ones that will face Turkish side Istanbul Basaksehir in the next round.
But Vokes’ vital away goal may just have given Burnley the edge after a fiercely contested tie which may yet also have a bearing on the Clarets’ Premier League campaign after goalkeeper Nick Pope sustained what looked a potentially serious shoulder injury.
When Pope was forced out of the action and the Clarets trailed it early on it threatened to be an even steeper learning curve in the ways of European football.
But a dominant second-half performance saw Burnley pass a major test of character and get a deserved equaliser through Vokes’ classy late finish.
In a dramatic start to the Clarets’ first European tie in 51 years, Burnley found themselves a goal and a goalkeeper down inside the first 20 minutes.
And it was wretched luck for Pope in a dramatic change of fortunes just a couple of weeks after he had been part of the England squad that had reached the semi-finals of the World Cup.
Pope would probably not have played had Tom Heaton not been ruled out with the calf injury that curtailed his appearance in Monday night’s friendly at Preston.
But his rapid return to action proved short-lived as he was hurt in a goalmouth scramble as Aberdeen piled on the early pressure.
Yorkshire-born targetman Sam Cosgrove challenged the Clarets’ keeper for a deflected cross which looped down under the crossbar and when the ball fell loose, Pope was injured as he palmed the ball away from in-rushing Dons midfielder Lewis Ferguson.
Lindegaard came on to make his Burnley debut – 10 months after signing following the shoulder injury that sidelined Heaton for much of last season – and having barely touched the ball he was forced to face a 19th-minute penalty.
Despite apparently minimal contact James Tarkowski was penalised for an aerial challenge on Cosgrove and Mackay-Steven accepted the chance to slot his spot-kick past Lindegaard, whose last European action had been a Champions League tie with Manchester United in November, 2012.
The goal further lifted a vociferous home crowd hoping to see only a second win over English opposition in 13 attempts in European competition.
Their side – second in the Scottish Premiership for the past four seasons - responded by making it a tough opening half for the Clarets, getting men behind the ball and then launching a series of dangerous counter-attacks through widemen Mackay-Steven and Niall McGinn.
Dyche’s side, backed by almost 2,000 fans, took their time to get a grip on the occasion before managingdid manage to gain a measure of control as they saw more of the ball just before half-time.
But efforts off target from Chris Wood and Johann Berg Gudmundsson didn’t really threaten an equaliser.
And it took until five minutes into the second half for the Clarets to go close to an away goal – Jack Cork somehow being denied by a stunning save from Joe Lewis.
Aberdeen paid tribute to former player Neale Cooper and celebrated the life of the midfielder from their 1983 European Cup Winners’ Cup winning side who died in May
The visitors had set the tempo from the re-start and when Gudmundsson whipped a ball in from the left Cork thought he had scored with a diving header before England under-21 international Lewis stuck out a hand to parry – the dangerous Aaron Lennon firing the loose ball back across the face of goal with Tarkowski just unable to get a touch.
Aberdeen’s primary target now looked to be to protect their clean sheet and extend an unbeaten record of eight home games in Europa League qualifying – although Lindegaard did have to save from Cosgrove following another break-away.
And the Danish international was called into action again with 65 minutes gone to make a vital save, diving full length to turn a header from Mackay-Steven round the post.
At the other end, Gudmundsson hooked a volley just over the bar moments after Dyche had sent on Vokes and switched to 4-4-2 formation with Vokes then heading a deep cross from Stephen Ward into the side netting as Burnley pressed for an equaliser.
And with 10 minutes to go Vokes provided it, showing great strength and determination to put Burnley level in the tie.
Tarkowski provided the delivery into the penalty area and when Woods picked out his strike partner, Vokes lifted the ball over his shoulder, shrugged off two defenders and volleyed into the roof of the net.
It was another vital strike from a player who has made a habit of coming off the bench to inspire his team.
And Vokes' historic goal - a first in Europe by a Burnley player since Brian Miller scored in both legs of the 1967 Fairs Cup defeat to Eintracht Frankfurt - sent the Clarets’ travelling fans away happy at the start of a long journey they hope will still have plenty of miles left to run in Europe yet.
Burnley: Pope (Lindegaard 14), Lowton, Tarkowski, Mee, Ward, Cork, Westwood, Lennon, Hendrick (Vokes 67), Gudmundsson, Wood. Substitutes: Taylor, Walters, Wells, Bardsley, Long.
Booked: Tarkowski, Lowton
Aberdeen: Lewis, Logan, Devlin, McKenna, Hoban, Ferguson (Gleeson 57), Ball, Shinnie, McGinn (Wright 79), Cosgrove (May 76), Mackay-Steven. Substitutes: Cerny, Forrester, Campbell, Anderson.
Referee: Daniel Siebert (Germany)
Attendance: 20,313 (Burnley 1,969)