The powerful young striker effectively booked the Dons place against Rijeka in the third round of qualifying for the fifth time in the last six seasons before even a quarter of this second leg tie was played.
By then someone who had only scored twice in eleven months after signing for a modest fee from Carlisle United in January 2018 scored as many in the opening 20 minutes against their shell-shocked Georgian opponents.
Then before the end he completed a hat trick that took his tally to six in the four European games played already this season, at the same time joining Pittodrie legend Drew Jarvie as the only Aberdeen player in their 52 year history of continental competition to score in four successive games.
Overall it's now an amazing 25 goals in 32 appearances since last December and Hearts won't be in any doubt who the main threat will be when they travel north to start their league campaign on Sunday.
What's more they were top quality team goals that suggests Aberdeen's new look side with four summer additions starting last night are gelling in a way that will once again make them the main threat to the Old Firm this season.
Besik Dekanoidze had caused a moment of anxiety with a shot Joe Lewis was happy to hold after just 34 seconds but that was about it from the visitors who had no answer to the home side's pace and precision.
The only surprise was that it took nine minutes for Aberdeen to hit the front such was their dominance but it was a goal to savour following a sweeping move involving Lewis Ferguson, Ryan Hedges, Niall McGinn and Jon Gallagher before Cosgrove scored with the aid of a deflection.
If anything the second, 11 minutes later, was even sweeter as Ferguson caught Shay Logan's probing pass down the right with a wonderful volleyed cross that Cosgrove sent soaring into the net with a diving header.
Then with ten minutes Cosgrove rounded things off by showing real composure when bending a shot round the goalkeeper with the outside of his right foot to make sure of heading home with the match ball as Aberdeen matched their best ever result in Europe under McInnes, the 5-0 drubbing of Daugava Riga five years ago.
Throughout McGinn, making his 300th start for the club since Craig Brown first signed him on a free transfer from Celtic, continued to prove that for all the comings and goings since, he remains one of the key players at Pittodrie.
Of course that included a short spell in South Korea for the Northern Ireland international but his best form has been in a red jersey and his whipped cross early in the second half nearly led to a third goal.
Dino Hamzic spilled the ball straight to Gallagher but the Chikhura Sachkhere goalkeeper redeemed himself with a marvellous reaction save at the feet of the versatile player on loan from MLS club Atlanta United.
Not that a rampant Aberdeen were to be denied for long as Ferguson's precision delivery from wide areas was exploited by Greg Leigh as the left back on from NEC Breda marked his debut with an adroit headed goal in 58 minutes.
Shortly afterwards McGinn was taken off, no doubt with the Premiership opener against Craig Levein's side in mind, only for his replacement to show the strength in depth McInnes has at his disposal now.
Scott Wright was only on for two minutes when he raced on to a Gallagher through ball to finish in style and claim his first goal since spending the second half of last season on loan at Dundee before Cosgrove rounded things off before departing to a standing ovation.
That, and a clean sheet for side that conceded more home league goals than St Mirren last season, made it a good night's work when you consider Mikey Devlin, Ash Taylor, Craig Bryson, Curtis Main and James Wilson didn't even make an appearance for a variety of reasons.