The Clarets are only one more win away from the group stages of the Europa League after again saving the best until last to earn another extra-time win.
After knocking out Aberdeen inside an added half-hour at Turf Moor, Sean Dyche’s battlers did it again to send Istanbul Basaksehir the same way and advance to the play-off round and two-legged showdown with multiple former Greek champions Olympiakos.
And once again it was Jack Cork who provided the catalyst for another landmark victory to extend the European tour in nerve-biting style.
This time Cork came off the bench as Dyche juggled his resources ahead of Sunday’s home Premier League opener against Watford.
And in the first half of extra-time he repeated his goal against the Dons with another top-class effort – this time with a crisp right-footed strike to kill of a Turkish side that in 210 minutes of football couldn’t find a way past Burnley’s rock solid defence.
The Clarets had never drawn a European tie at Turf Moor before, winning six times and losing only once - a defeat to Eintracht Frankfurt ending their last run in European competition 51 years.
And the only draw that would potentially take Burnley through this time from the third qualifying-round tie would be a repeat of the 0-0 scoreline in Turkey a week ago followed by the possibility of a penalty shoot-out.
The Clarets therefore needed a goal to avoid that scenario and maintain Basaksehir’s record of never having kept a clean sheet in their previous eight away games in Europe.
And in a first half largely dominated by the home side it nearly came on a couple of occasions in 45 minutes which combined a mixture of promise and frustration in equal measures.
With the Turkish side in no hurry to do anything and the Romanian referee punishing virtually any physical contact momentum was hard to find.
But the Clarets – with five changes to the starting line-up from the first leg and Ashley Westwood captaining the side for the first time – made it fairly apparent they were eager to get the ball forward early and exert the kind of pressure they sacrificed in the first leg.
And 10 minutes in it was the physical presence of Barnes that created the first chance. This time the striker did get the benefit of the doubt from the officials after leaving defender Alexandru Epureanu on the floor but he failed to capitalise thanks to a wayward shot into the side netting.
Burnley’s pressing game was making it a tough night for Basaksehir goalkeeper Mert Gunok, whose distribution started to fail under pressure.
And twice it nearly proved costly for his team before he redeemed himself with smart saves from Phil Bardsley and Aaron Lennon, who also combined well to set up a shooting chance for Sam Vokes, which was blocked.
Firstly, Gunok turned away a fierce drive from Phil Bardsley and then following a superb run by Lennon he saved with his legs after the Clarets’ wingman had weaved his way through the visiting defence to earn a clear sight of goal.
Basaksehir didn’t look to be enjoying the occasion, but knowing that an away goal would put them in control of the tie they enjoyed a purple patch just before the break that almost saw them take the lead.
And it was dangerman Edin Visca – the Turks’ best player along with skipper Emre in the first leg – who provided the threat.
It took a superb save from Joe Hart on his home debut, diving to his left at close range to keep out the winger’s best effort, before former Fulham midfielder Kerim Frie also tested the England international in stoppage time.
The Clarets heeded the warning shot and seven minutes into the second half should have gone in front.
With the visitors suddenly being stretched down both flanks and the Clarets’ fans urging their side on, Westwood delivered a perfect cross from the left which curled beyond the Basaksehir defence but was headed over the bar by Barnes from inside the six-yard box.
Vokes then saw a header from substitute Johann Berg Gudmundsson held by Gunok but it was no longer one-way stuff and as time ticked away, the jeopardy of an away goal increased.
Visca again nearly provided it with a skidding drive which Hart turned around a post at full stretch but as the Clarets pushed for a late winner themselves they had a penalty appeal for handball turned down as Barnes tried to force his way through with the last sniff of a chance before extra-time for the second tie running.
Then Cork had struck the crucial goal to see off Aberdeen’s challenge and the Clarets’ leader did again in stunning style eight minutes into the first period.
Having been a given a rare breather, Cork took over the captain’s armband when he replaced Westwood and the midfield man led by example with a magnificent finish, curling the ball into the top corner from almost 25 yards after Jeff Hendrick had kept a cool head to set up the chance after more Burnley pressure had forced an error.
It was then a case of seeing the game out, as Kevin Long produced a peerless performance in a new-look central defensive partnership alongside debutant Ben Gibson.
And with the tireless Bardsley and Stephen Ward also digging in to help Hart keep a third successive clean sheet, it was mission accomplished as Hart's final big save from a Visca header in stoppage time made it all aboard for Athens in a week’s time.
Burnley: Hart, Bardsley, Long, Gibson, Ward, Lennon (Gudmundsson 58), Westwood (Cork 82), Hendrick, Taylor, Barnes (Tarkowski 120), Vokes (Wood 82). Substitutes: Legzdins, Lowton, McNeil.
Booked: Long, Gibson, Ward
Istanbul Basaksehir: Gunok, Clichy, Epureanu, Da Costa, Caicara, Belozoglu, Tekdemir (Inler 92), Frei (Napoleoni 102), Kahveci (Jojic 119), Visca, Bajic (Adebayor 66). Substitutes: Babacan, Attamah, Ucar.
Referee: Istvan Kovacs (Romania)