Aberdeen’s expansive, slick football destroyed Chikhura Sachkhere to equal the best Euro run under boss Derek McInnes.
The Reds’ dominant destruction set up a third qualifying round clash with HNK Rijeka, with the first leg in Croatia on Thursday.
Aberdeen have never progressed beyond that third qualifying round under McInnes but have a real opportunity to change that this season.
The intensity, movement and speed of both thought and play from the Dons left the Georgians chasing shadows for most of this one-sided contest.
If they can reproduce this level against HNK Rijeka the Reds will have a great opportunity of progressing. And after that there is only one more phase, the play-offs, before the lucrative group stages.
There will be far tougher teams and challenges ahead, starting with the Croatians, but the Dons brutally exploited the gulf in class against Chikhura.
The pace and fluidity of their play, with the new signings gelling, bodes well not just for the Europa League but the domestic campaign.
Aberdeen face Rijeka with the knowledge they knocked the Croatians out of the Europa League 5-2 on aggregate in 2015, with a memorable 3-0 away victory.
The Croatian Cup holders are sitting joint top of their top flight with a maximum six points from their opening two games.
Rijeka face NK Slaven Belupo Koprivnica at home tomorrow and boss McInnes will have that match scouted. Crucially Rijeka are playing out of the 8,279-capacity Stadion Rujevica and not the Kantrida Stadium where the Dons triumphed four years ago.
The Kantrida, which is out of use while being rebuilt, had been a fortress for Rijeka when the Dons ended a near two-year unbeaten home record.
At Pittodrie, the Georgians were the first to threaten after just 34 seconds. Besik Desanoidze fired in a 20-yard shot but keeper Joe Lewis easily saved.
After that it was incessant Dons pressure which paid off with the opener in the ninth minute from a superb passing move.
Midfielder Lewis Ferguson picked out Ryan Hedges who slalomed into the box before squaring a pass to Niall McGinn.
The winger then found Jon Gallagher to his left who rolled a pass to Sam COSGROVE.
Striker Cosgrove checked inside then fired in a low 12-yard drive which took a deflection and flew beyond keeper Dino Hamzic.
Aberdeen were flooding forward at will with fluid, interchanging football and an inevitable second arrived in the 20th minute.
It was a superb goal as Logan fired a cross-field pass to Ferguson whose first time volleyed cross along the face of goal found COSGROVE. The striker headed home from five yards.
In the 58th minute it was 3-0 when Ferguson whipped in a cross to LEIGH who headed from six yards into the left corner.
The fourth goal in the 64th minute was another cracker with Gallagher playing through substitute Scott WRIGHT. Collecting the ball on the run, Wright expertly guided it with a sweeping low first touch beyond the keeper.
COSGROVE secured his hat-trick in the 80th minute when he collected a pass from Logan and out-muscled a defender before stabbing home from 15 yards.
Cosgrove has now netted in all four Euro ties to take his tally for the season to six goals.
Never mind Scott McKenna, on this form the concern for Aberdeen could be an English club coming in with a bid for Cosgrove before their transfer window closes at 5pm on Thursday.