The visitors were forced to play 85 minutes of the match with 10 men after Sylvain was sent off for conceding an early penalty, and a goal in either half from Jouffre secured the hosts the win.
© Getty Images
Rennes got off to the worst possible start when Armand was issued a straight red card for bring down Vincent Aboubakar in the penalty area from behind to prevent a clear scoring opportunity.
Jouffre comfortably slotted home the resulting spot kick to get Lorient off to a great start.
Despite having a one-man advantage, Lorient failed to add to their lead and went into the break ahead by just the single goal.
The visitors went close once again on the hour mark from a free kick, but Nelson Oliveira headed off target from the cross into the box.
Lorient had a chance to kill the game off with 25 minutes to go when Jouffre linked up well with Jeremie Aliadiere, but the former could only shoot straight at Costil after receiving the return pass.
However, Lorient made sure of the win just three minutes from time when Jouffre sliced a swerving effort into the bottom corner from the edge of the box after good build-up play.
Lorient are 10th in Ligue 1, while Rennes stay in 12th place.