Payet netted after seven minutes and Radonjic doubled the lead late on to put Marseille on 46 points from 23 games, a distant 12 behind leaders Paris St Germain but with a healthy advantage over third-placed Stade Rennais.
The kickoff was delayed by 15 minutes after the players were affected in their warmup by tear gas used by the police during a fight between opposing fans outside of the stadium.
Marseille were quick off the mark, however, as Payet beat Stephane Ruffier from just inside the box.
Radonjic put the result beyond doubt five minutes from fulltime with a low angled shot.
St Etienne are 15th on 28 points.
Lyon's hopes of securing a Champions League spot for next season were hit when they were held to a goalless draw at home by lowly Amiens.
Rudi Garcia's team are sixth on 33 points, seven points behind Rennes.