Payet, a summer signing from Lille, became only the fifth player to score a brace on his debut as Marseille beat Guingamp 3-1 last week and he was on the scoresheet again on Saturday, slotting home a low left-footed shot just after the hour mark.
Andre-Pierre Gignac, who also opened his account for the new season last week, had broken the deadlock in the 15th minute as Marseille made Evian pay for missing a host of chances.
Nice atoned for an opening-day humiliation by securing their first points of the season from a 2-1 victory over 10-man Rennes.
Dario Cvitanich saw his 20th-minute opener cancelled out by Nelson Oliveira just before the break but Jeremy Pied would hit what proved to be the winner following the restart.
Rennes winger Vincent Pajot was then dismissed at the death for a professional foul on Valentin Eysseric.
Israel international Eden Ben Basat earned Toulouse a point from a 1-1 draw with Bordeaux as both sides continue to look for their first win of the season.
The visitors opened the scoring through Cheick Diabate - the Mali international scoring two minutes before half-time - but held the lead for barely two minutes as Ben Basat chimed in.
St Etienne are one of three sides with a 100 per cent record after victory over Guingamp.
Les Verts sit behind Lyon and Marseille on goal difference, with Fabien Lemoine's second-half goal enough for a narrow 1-0 win.
Two late goals from Gianni Bruno and Adama Ba earned Bastia their first three-point haul of the new season after they saw off the challenge of Valenciennes in a 2-0 win.
Valenciennes came into the match having beaten Toulouse 3-0 first time out while Bastia had lost 2-0 at promoted Nantes, but it was Frederic Hantz's men who were celebrating tonight thanks to Bruno and Ba.
Bruno opened the scoring in the 78th minute and Ba added a second two minutes later with a diving header to seal the victory.
Reims claimed their first win this season at home to Lille as Mads Albaek's early score and Christopher Glombard's second-half scrambled strike settled a 2-1 victory.
Albaek put the home side ahead with a seventh-minute rocket before Glombard sealed the win midway through the second period, with Marko Basa's 88th-minute score for Lille only a late consolation.