Angers defender Arnold Bouka Moutou put through his own net in injury time to hand Rennes a deserved 1-0 Ligue 1 victory.
Rennes dominated much of the game at Roazhon Park on Friday, but looked set to be frustrated by a well-drilled Angers outfit.
However, a flurry of late corners for the hosts eventually led to Angers' resistance being broken by one of their own men in the 91st minute, as Bouka Moutou inadvertently diverted a set-piece beyond the helpless Denis Petric.
Rennes had a goal disallowed for a foul on goalkeeper Petric shortly before half-time, before Ousmane Dembele hit the post with an excellent low drive from 20 yards.
Petric made a superb save with two minutes remaining, but there was nothing he could do about substitute Bouka Moutou's costly error.
The win means Rennes leapfrog Angers into fifth place in Ligue 1, one point behind Saint-Etienne.