Rennes was down to 10 men by the fifth minute when center back Sylvain Armand was sent off for fouling Vincent Aboubakar. Lorient midfielder Yann Jouffre converted the subsequent penalty and scored with a low strike in the 87th.
Guingamp midfielder Younousse Sankhare scored the equalizer in the 71st to salvage a 1-1 draw with lowly Valenciennes after Tongo Hamed Doumbia put the hosts ahead with a header in the 17th.
The match between Saint-Etienne and Evian was postponed because of a frozen pitch.
PSG had a 36-game unbeaten run snapped by a 2-0 loss to Evian on Wednesday. The defending champion showed more desire on Saturday while making increased efforts to track back.
"We wanted to react after the loss at Evian," PSG goalkeeper Salvatore Sirigu said. "We realized we made some mistakes. We did not give 100 percent physically and mentally on Wednesday."
PSG capitalized on Ibrahimovic's fifth assist this season to open the scoring and could have reached the interval with a bigger lead. But Sochaux centerback Carlao blocked close-range efforts from Blaise Matuidi in the fourth and Motta in the 21st.
Cros then frustrated PSG by stopping low strikes from Ibrahimovic in the 26th and Cavani in the 44th.
PSG pressed high up the pitch to double the lead shortly after the break before Cavani trapped a ball over the top from Ibrahimovic to notch his 11th league goal with a side-footed effort.
A short drop in intensity allowed the visitors to create a couple of chances. But the low drive from Sochaux substitute Rafael Dias in the 68th lacked power to trouble Sirigu, who parried Emmanuel Mayuka's volley from a tight angle in the 70th.
Sochaux center back Mathieu Peybernes stopped a play from Ibrahimovic by handling the ball. But the Sweden striker unleashed the subsequent free kick into the top corner from 20 yards to make it 4-0.
Ibrahimovic then consolidated his spot as the top scorer in the league by converting a low cross from Cavani for his 13th goal.
"He sets an example to our young players," PSG coach Laurent Blanc said about Ibrahimovic. "The whole team is energized when it sees Zlatan wanting to win, score and give the final ball."
On Sunday, second-place Lille visits Bordeaux, Monaco hosts Ajaccio, Lyon faces Bastia and Montpellier plays Toulouse.