After taking an early lead, the Gunners conceded twice after Sokratis Papastathopoulos was sent off in the first half.
Arsenal boss Unai Emery named a strong starting line-up that included Pierre-Emerick Aubameyang, Mesut Ozil and Lucas Torreira.
The north London outfit got off to the perfect start, scoring in just the third minute to make it 1-0.
Alex Iwobi collected the ball on the left and created some space for himself before sending in a cross that travelled untouched into the back of Rennes’ goal.
The centre-back received two yellow cards in the space of seven minutes, the second of which coming after he pulled Ismaila Sarr down as the Rennes attack burst through.
Benjamin Bourigeaud took the resulting free-kick and, after his initial effort hit the wall, he smashed a soaring effort past Petr Cech to make it 1-1.
The hosts made the brighter start to the second half, putting Arsenal under serious pressure.
Cech was called into action more than once, the goalkeeper frustrating his former club with a string of saves.
But Rennes’ pressure eventually told when, in the 65th minute, Nacho Monreal scored an own goal.
The left-back was left red-faced after he deflected Mehdi Zeffane’s cross into his own net.
It was all that the French side deserved.
They added a third in the 88th minute through Sarr to cap an incredible night for the Ligue 1 outfit.
Arsenal were unable to find an equaliser and it means they have to win when the two sides meet in the return leg at the Emirates Stadium on March 14.
The Europa League may represent Arsenal’s best hopes of qualifying for next season’s Champions League, so victory is crucial.