In the day's early fixtures, Monaco eased their relegation woes with a last-gasp 3-2 defeat of Rennes while Bordeaux suffered a 1-0 setback against visiting St Etienne.
Kamara netted a third-minute opener for 1993 European Cup champions Marseille, blasting a deflected shot past keeper Matz Sels after Strasbourg failed to clear a low free kick driven into the area from the left.
Dutch midfielder Strootman sealed the win with a stoppage-time penalty after Benedetto was brought down by a visiting defender.
The result left Marseille fourth on 16 points from 10 games while Strasbourg stayed bottom on nine points.
Wissam Ben Yedder scored a 90th-minute winner for Monaco to cap a memorable evening after giving his side an early lead in a roller coaster, as the visitors hit back through Faitout Maouassa and Adrien Hunou.
Algeria striker Islam Slimani, on loan at Monaco from Leicester City, levelled in the 56th minute before Ben Yedder delighted the home fans as the principality side moved up to 14th place, two points clear of the bottom three.
A 90th-minute penalty from Denis Bouanga gave St Etienne a surprise win at sixth-placed Bordeaux and allowed the visitors to move up to 10th place.