After Dimitri Payet's 84th-minute free kick was saved by goalkeeper Edouard Mendy, Strootman showed good balance to clip the loose ball high into the net from a tight angle just two minutes after coming off the bench.
Marseille is nine league games unbeaten and four points behind league leader Paris Saint-Germain, which has played two games less, and eight clear of Rennes, which plays its game in hand at 19th-place Nimes on Wednesday.
In a tight and physical contest, Marseille center half Alvaro Gonzalez hit the post from 15 meters out following a bizarre corner in the 42nd minute. When Mendy went to clear a routine back pass, the ball hit one of several lumps of crumpled paper thrown from the Rennes fans behind his goal and bobbled up and over his foot for a corner.
Benjamin Bourigeaud's curling shot from just outside the area drew a sharp save from Marseille goalie Steve Mandanda just before halftime. Tempers frayed as players confronted each other in the tunnel at the interval, and the start of the second half was delayed by several minutes.
Rennes forward Raphinha went close with a half-volley from just inside the area which fizzed past the left post in the 67th. Moments later, Mendy kept out a low drive from Payet from a similar distance.
PSG hosts Monaco on Sunday in coach Robert Moreno's first league game in charge of Monaco. He replaced Leonardo Jardim, who was fired by Monaco for a second time.