Alex Iwobi gave the Gunners a perfect start in north-western France at a raucous Roazhon Park, but the match hinged on the sending-off of Arsenal defender Sokratis Papastathopoulos four minutes before half-time.
Benjamin Bourigeaud equalised moments later, and the hosts' second-half pressure paid off as a Nacho Monreal own goal put Rennes ahead before Ismaila Sarr's late header gave them a two-goal cushion in the tie.
Unai Emery's side must now turn the tie around in the second leg in London next Thursday if they are to progress any further in a competition which represents their only hope of silverware this season, and offers a potential route into next season's Champions League with Arsenal sitting outside the top four in the Premier League.
"I think we can do better, 3-1 is hard for us," said Emery.
"We are going to think for next week. We will start with 11 against 11, without Sokratis, without (Alexandre) Lacazette, but if we play like we did in the first 40 minutes, with our supporters also, we will have the possibility to come back."
The Gunners recovered from a first-leg deficit to beat BATE Borisov in the last round, but Rennes are a step up in quality and are revelling in what is already their best ever European run.
- Sokratis sent off -
After Iwobi's early opener, the game turned just before half-time when Hatem Ben Arfa played in Sarr, who was hauled back by Sokratis just outside the area. The Greek defender had already been booked, so a second caution equalled a red card.
Bourigeaud struck the wall from the resulting free-kick, but the ball came back to him and he sent a stunning half-volley into the far corner.
Petr Cech, back facing one of his former clubs, made several interventions before being beaten again in the 65th minute, as Mehdi Zeffane's cross from the right deflected in off Monreal, and Sarr added the potentially crucial third goal two minutes from time.
- Chelsea cruise -
Chelsea may also need this competition to get back in the Champions League next season and the Blues eased past Dynamo Kiev 3-0 at Stamford Bridge courtesy of goals from Pedro Rodriguez, Willian and Callum Hudson-Odoi.
Pedro could have had at least a hat-trick as Denys Boyko denied him four times after the Spaniard had turned home Olivier Giroud's flick to give Chelsea an early lead.
Willian was more accurate with a brilliant free-kick 25 minutes from time to double Chelsea's lead and substitute Hudson-Odoi surely put the tie beyond Kiev with a smart finish a minute from time.
"The third goal for us is really very important," said Chelsea manager Maurizio Sarri.
"3-0 is an important result, but of course we have to play the second leg so we have to be careful."
Sarri's former side Napoli are also well on course for the quarters as early goals from Arkadiusz Milik and Fabian Ruiz, plus a second-half own goal from Jerome Onguene, earned a 3-0 win over last season's semi-finalists Salzburg.
Valencia beat Krasnodar thanks to Rodrigo's double at the Mestalla, but Viktor Claesson's second-half strike will give the Russians hope of reaching the last eight on home soil in the second leg.
Inter Milan could regret a missed penalty by Marcelo Brozovic as the Italian giants drew 0-0 away to Eintracht Frankfurt.
Sevilla won the Europa League three years in a row between 2014 and 2016 with Emery as coach, but the most successful side in Europa League history have work to do after twice blowing a lead to draw 2-2 at home to Slavia Prague.
Villarreal have now won as many games in the Europa League as La Liga this season. Despite languishing in the relegation zone of the Spanish top flight, a 3-1 win away to Zenit Saint Petersburg put them within touching distance of the quarter-finals, while Dinamo Zagreb beat Benfica 1-0.