Alex Iwobi gave the visitors a perfect start before the host drew level through Benjamin Bourigeaud strike and things went from bad to worse for the Gunners as defender Sokratis Papastathopoulos was sent off for a second bookable offence.
Rennes added two more goals after the break to remain in control of the fixture heading to return leg at the Emirates. Elsewhere Chelsea beat Dynamo Kiev three nil.
Arsenal are in big trouble and only a remarkable salvage operation at the Emirates next week can keep their Europa League hopes alive.
The problem for manager Unai Emery is that Rennes are a team brimming with swagger and ability - and they look more than capable of finishing the job in the second leg.
Emery will back his team to reach the quarter-finals but on this evidence - despite playing with 10 men following Sokratis' sending off just before half-time - overturning the deficit could well be beyond Arsenal.
Emery said: 'We know it's a bad result and it's going to be tough. It's not a good experience because we couldn't do our work in difficult minutes with one less player.'
In France for the first time since leaving Paris Saint-Germain, Emery fielded a strong team that included Mesut Ozil, whose reintegration under the Spaniard appeared to be gathering pace until this showing.
Ozil reverted to type - crumbling at the first sight of difficulty. Emery feels he cannot trust Ozil on tough away days and it is easy to see why.
Rennes have their own maverick, of course. Hatem Ben Arfa, who fell out with Emery in the pair's time together at PSG, started for the French side.
He said: 'I saw the same Emery, as agitated as ever. I looked over at him a few times and that made me laugh. He hasn't changed.'
But it was Ben Arfa's team-mate, Benjamin Bourigeaud, who stole the show. He was untouchable at times and starred in the game that was billed as the biggest occasion in the French club's 118-year history.