Yedder pounced on Keita Balde's flick two minutes into added time to lash home a powerful left-foot finish and send Leonardo Jardim's side up to 14th just as it looked as if a handball spotted by VAR had denied them the three points.
Balde thought he had won the game for Monaco seconds before when he capitalised on a dreadful error by Rennes goalkeeper Romain Salin to roll the ball into an empty net, only for the video assistants to spot him controlling the ball with his hand.
The last-gasp winner was Ben Yedder's eighth goal in as many league matches, putting him top of the Ligue 1 scoring charts and making fans forget Radamel Falcao's departure to Galatasaray.
"I'm very happy, it wasn't an easy match. We scored in the last seconds and it was a very good goal, so I'm very happy," said Ben Yedder.
Monaco started the weekend in 16th but dropped into the relegation playoff places before Sunday's match. It seemed they would stay there once Balde's goal was rightly ruled out.
The late goal means they are now level on 12 points with Toulouse, Amiens and 12th-placed Rennes, who have not won a match since August.
Monaco had taken the lead through Ben Yedder's smart finish after just two minutes.
However, a wonderful solo run and finish from Faitout Maouassa and Adrien Honou's tap-in put Rennes ahead just after the break.
Monaco levelled after the away side gifted the ball to Cesc Fabregas. The Spaniard rolled in Islam Slimani to score in the 57th minute.
"We came back to 2-2 when we could have lost, and that's good. It was hard work but often those matches are what do you good," added Ben Yedder.
Earlier, Claude Puel continued his perfect start as Saint-Etienne coach.
Denis Bouanga's stoppage time penalty at Bordeaux launched Puel's side into the top half of the table.
The 10-time French champions were second-bottom in Ligue 1 after their home loss to Metz late last month but have won three straight, the last two under Puel.
Their turnaround in form, which includes victory over local rivals Lyon in Puel's first match, has moved them to ninth, ahead of 10th-placed Marseille's clash with Strasbourg.
Bordeaux meanwhile missed the chance to move into the Champions League positions with their second home loss on the bounce.