Menez, who has lost his starting role this season, fired home in the 57th minute before league top scorer Ibrahimovic struck his 26th of the season in added time as PSG get ready to visit Barcelona in the Champions league on Wednesday.
PSG have 64 points with seven games left ahead of Olympique Marseille who beat visitors Girondins Bordeaux 1-0 on Friday.
"It was a very complicated game," PSG's France defender Mamadou Sakho told TV channel Canal Plus. "But we have a winning mentality - just see the team's reaction after the second goal. It shows our desire to go get this title."
Fourth-placed Nice stayed on course for a Champions League qualifying spot when Kevin Anin's injury-time goal secured a 4-3 win at Toulouse two minutes after Wissam ben Yedder equalised for the home side in the 90th.
Both teams finished with 10 men after Toulouse's Ali Ahamada and Alexy Bosetti of Nice were shown straight red cards for dangerous tackles in the final minutes.
PSG goalkeeper Salvatore Sirigu kept out Sadio Diallo's low shot in the 14th minute as PSG got started sluggishly but Rennes were slow to take advantage in a dull first half.
Menez, who has started on the bench for most of PSG's important games recently, was keen to make a point, showing the visiting fans his name on the back of his shirt after coolly slotting home following a dazzling run past the Rennes defence.
Beckham and Lavezzi, introduced for Marco Verratti and Kevin Gameiro respectively, also got into the action ahead of Wednesday's Nou Camp clash.
It was from Beckham's attempted chip with the outside of his boto in the 93rd minute that Ibrahimovic headed home although he appeared to be an offside position.
Meanwhile, Nancy kept their hopes of survival alive when Romain Grange's second-half goal gave them a 1-0 win against bottom club Troyes.
