Aberdeen went ahead in the 92nd as Matty Kennedy grabbed his first goal for the Dons, before Eamonn Brophy drew Kilmarnock level later in the first additional period.

Kilmarnock then thought they had won it as Nicke Kabamba put them 3-2 up in the 117th minute, but moments later Aberdeen substitute Sam Cosgrove made it 3-3 from the penalty spot after Stuart Findlay had upended Lewis Ferguson.

Then, in stoppage time, Killie sub Connor Johnson inadvertently diverted a Considine cross beyond goalkeeper Laurentiu Branescu to seal a 4-3 win for Aberdeen.

And McInnes was full of admiration for the never-say-die spirit of his players.

McInnes said: "Obviously I've got pride in the players' tenacity to keep going. They never gave it up.

"There are different ways to win a match. You can do it tactically, which we didn't do tonight, you can do it through big moments individually, or you can just do it with sheer guts and tenacity and a refusal other than to make the game go our way.

"That's where we were. We made the three changes at half-time, don't see three too often.

"It was a bit of a risk but one we needed to take.

"Second half, if we'd lost 1-0 it wouldn't have been for the want of trying.

"Thankfully, big Andy gets on the end of one of many crosses and takes us to extra time.

"The last goal for them was a calamity goal, it wasn't even a dangerous situation.

"But with Lewis Ferguson, the bigger the game, the bigger the performance, and when the game needed a big moment he produced as he had the courage to drive in and make something happen and he got us the penalty.

"That was a lifeline for us and Cosgrove got the equaliser and then just as we're sorting out the order for penalties, I had my five ready, Andy's running down the line like Ryan Giggs.

"It was no more than we deserve and when you see 1,200 fans celebrating and the club coming as one, we've needed that connection and that performance.

"It's almost as though we've lit a fire under our season now."

Kilmarnock manager Alex Dyer admits they threw away the tie.

Dyer said: "It's hard to put into words. We had the game sewn up and we threw it away. They're a good side and if you give good sides a sniff they punish you and that's what they did.

"We should have put the game to bed.

"But we got to a point where the game was won. We made bad decisions at key moments. I'm gutted for the fans because we let them down."