Cork gobbles up his chance to give the Clarets a Turkish delight
The midfielder spoke passionately about his experience so far in the aftermath of the Clarets' goalless draw with Southampton at St Mary's at the weekend.
The 29-year-old was named as a substitute for the second leg against Istanbul Basaksehir at Turf Moor but you could see the fire burning brightly in his belly as soon as Ashley Westwood made way for him in the 81st minute.
The former Chelsea man got the ball rolling in extra-time against Aberdeen, converting Charlie Taylor's cross to seal Burnley's passage to this stage, so it was quite apt that he would be the match-winner once more.
Cork doesn't score many goals with his feet. The England international doesn't score many goals from outside the box. So it seemed completely against the grain when he swept home Jeff Hendrick's assist from 20 yards out in the 97th minute.
As soon as the ball left his boot there seemed only one likely destination. And so it proved.
Cork's finish was immaculate, perfectly weighted, carrying a good height, travelling just out of reach of Mert Gunok as it reached the top corner.
Substitute Johann Berg Gudmundsson was also involved in the build up, Hendrick cleared the path on the edge of the box with a clever dummy and the former record signing picked out Cork who took care of the rest, setting up a two-legged tie with Greek outfit Olympiakos.
Former Arsenal and Manchester City striker Emmanuel Adebayor could also have played his part on the bench as the hosts defended their delicate advantage.
You'd have backed the Togolese international to bury his header from the position he'd got himself in to from Irfan Kahveci's delivery but the forward directed the ball over the bar.
The visitors almost stole it at the end of the additional 30 minutes when Edin Visca flicked a header on target but Joe Hart wasn't about to concede his first goal since signing at that moment, dropping to his left to turn the ball around the woodwork.
The two sides, who played out a 0-0 draw at the Fatih Terim Stadium a week ago, failed to find the net again in normal time, meaning Olympiakos will have to wait a short time longer to find out who their opponents will be in the play-off.
What we have learned from the last two games is that Burnley will be very hard to beat again this season but they'll need to be more ruthless in front of goal if they are to make life a bit more comfortable for themselves.
After squandering a number of golden opportunities to claim all three points in the Premier League opener against Southampton at St Mary's, the Clarets were wasteful once more.
A sequence of profligacy was opened by Ashley Barnes who, when given the benefit of the doubt by Romanian official Istvan Kovacs following a challenge on Alexandra Epureanu, chose the wrong option when shooting in to the side-netting while team-mates screamed for the ball inside the penalty area.
Phil Bardsley couldn't have done much more when hitting the target from 25 yards out but Mert Gunok saw the ball all the way and did what was expected of him when beating it to safety.
Barnes skied another attempt later on when strike partner Sam Vokes rose highest to win the flick on before the Welshman was foiled by a wall of bodies from close range once Aaron Lennon's cross found a way through.
Lennon hasn't netted in almost two years, since scoring in a 4-0 win over Yeovil Town for Everton in the League Cup and he might not craft a better opportunity than the one he failed to convert just before the half hour.
Just like the chance that fell to him on the South Coast, which goalkeeper Alex McCarthy saved, Lennon couldn't find a way past with only Gunok to beat.
The opening came from the Istanbul Basaksehir stopper's mistake, when his delayed clearance was closed down by Barnes, but the 29-year-old, who has six caps for Turkey, made amends when saving with his legs after Lennon wriggled clear.
That brought a change in momentum as the visitors started to come out of their shell in search of the away goal that would give them a clear advantage.
Edin Visca tested the water with a shot that cleared the crossbar from the edge of the area after turning debutant Ben Gibson and maneuvering the ball on to his left boot.
The Bosnian international threatened again, this time with his other foot, after Hendrick conceded possession in his own half, but Hart repelled the effort.
The tie was soon transforming in to a battle between those two but Hart, who headed in to the fixture on the back of two clean sheets, came out on top again when the odds seemed stacked against him.
When Kerim Frei got in behind Bardsley to hit the bye-line, where he rolled the ball in to the six yard box, the hosts looked destined to fall a goal behind when Visca got ahead of Kevin Long to steer goalwards, but Hart reacted well to block to his left.
The former Manchester City goalkeeper, who has won the Premier League Golden Glove award four times, was quickly repaying Sean Dyche's faith in him and he displayed his agility once more with a save from Frei at the foot of his right hand upright.
Hart's former team-mate, Gael Clichy, forced another chance before the half was up, with the full back's low drive taking a nick but Hart was equal to the attempt.
The home side, who bypassed Aberdeen in the Battle of Britain to reach the third qualifying round, found a way beyond their opponent's backline early in the second half and they really should have capitalised.
Epureanu and Manuel da Costa were caught flat-footed from Ashley Westwood's mouth-watering in-swinger but, with just yards separating Barnes from Gunok's goal, the striker powered his header over the bar.
Vokes then managed to wriggle clear of his marker to meet substitute Johann Berg Gudmundsson's corner but Gunok clawed on to his header in mid-air.
Hart's vendetta against Visca resumed after the hour and this one was probably the pick of the bunch. The away side's star man collected Junior Caicara's pass inside the box and fired across Hart, targeting the far corner, but the Three Lions keeper drew on his experience and height to get a fingertip to the ball and turn it around the post.
Irfan Kahveci wasn't far away from sending the Turkish side through in normal time when his half-volley gathered speed on the turf but the ball drifted past the far post.
Then, in stoppage time, Barnes was up in arms, vociferously appealing for a penalty when Mahmut Tekdemir appeared to handle the ball, but Kovacs was having none of it.