The 20-year-old French striker started life as a permanent Celtic signing in the best way possible, setting Rodgers’ side on their way to an ultimately comfortable 3-0 win over Armenian champions Alashkert in Yerevan.
Passage to the second of the four qualifying rounds Celtic must negotiate this season is now little more than a formality in next Wednesday’s second leg in Glasgow.
Edouard’s first European goal on the brink of half-time settled any Celtic nerves as they delivered an assured display to take command of what had been regarded as a potentially hazardous assignment.
The Frenchman played a peripheral role on the European stage for Celtic while on loan from Paris Saint-Germain last season, making only two brief substitute appearances in the Champions League.
Much more will be expected of him over the coming campaign which he goes into wearing the label of Celtic’s most expensive ever signing.
His crucially timed contribution in first half stoppage time provided an encouraging early indication that he will not be unduly burdened by the price tag.
Edouard’s goal was an excellent indication of the predatory talent which has moved Rodgers to describe him as one the best young players in Europe.
He showed admirable composure and sharp reactions when James Forrest’s scuffed effort across the face of the penalty area fell into his path.
While the Alashkert players claimed in vain for a foul in the build-up, Edouard flicked out his left foot instinctively to steer the ball beyond the helpless Ognjen Cancarevic in the home goal.
Serbian goalkeeper Cancarevic had made two excellent interventions to deny Celtic an earlier breakthrough, keeping out a curling shot from Edouard’s compatriot and strike partner Moussa Dembele and then rushing from his line to smother another attempt from the same player.
It was always going to be a big ask for Celtic to hit the ground running in such difficult conditions. The temperature was officially recorded at 36 degrees by Uefa, allowing for the provision of water breaks during the match.
The gratification on the faces of the Celtic players when they first of them came on the half hour mark underlined just how draining a physical test it was.
In the absence of World Cup defenders Mikael Lustig and Dedryck Boyata, there was a raw and relatively inexperienced look to the Celtic back line, even if it did contain two recently fully capped internationals in Kristoffer Ajer and Jack Hendry.
There were occasions when Celtic’s defending was as shaky as the direction of the Armenian television pictures being provided to Premier Sports, posing a challenge for commentator Rob MacLean which he met with customary aplomb.
Hendry, making his European debut, almost handed Alashkert a route back into the contest in the opening minute of the second half when he dallied in possession on the edge of his own penalty area.
Jefferson Reis pounced on the error but the Brazilian striker lacked the conviction to fully punish it, managing only a tame shot which was comfortably gathered by Craig Gordon.
There had been little to really trouble the Celtic goalkeeper but he was eventually forced into a more demanding save when he reacted smartly to touch over a dipping long range effort from Artak Yedigaryan.
Edouard, his work very much done, was replaced by debutant Lewis Morgan in the closing stages of a satisfying evening for Celtic which was rounded off pleasingly by Forrest’s goal nine minutes from time.
The winger has a happy knack of scoring valuable goals in the Champions League qualifiers and he swept home another after Alashkert were unable to properly clear a Callum McGregor corner. Forrest returned the favour in the 90th minute, setting up McGregor for Celtic’s third which was a fair reflection of their superiority over limited opponents.