Wesley Said scored the winner after a Dimitri Payet double had cancelled out first-half goals by Florian Sotoca and Przemyslaw Frankowski to put Lens on 15 points from eight games. They trail leaders Paris Saint-Germain, who beat Montpellier 2-0 on Saturday, by nine points.
Third-placed Marseille have 14 points from seven games after their first defeat of the season. They have a game in hand, away to Nice after the encounter was abandoned amid serious crowd trouble last month.
At the Stade Velodrome, Sotoca put the visitors ahead on nine minutes, converting a penalty after Pape Gueye handled in the area.
Lens doubled their advantage through Frankowski, who slalomed down the wing before curling a superb strike into the far top corner in the 27th minute.
Marseille suddenly found their groove and by halftime they had levelled.
Payet first reduced the arrears on 33 minutes when he beat Jean-Louis Leca with a curling free kick.
Three minutes into first-half stoppage time, Marseille were awarded a penalty following a VAR review after Christopher Wooh fouled Bamba Dieng and Payet converted.
Marseille piled on the pressure in the second half and Cengiz Under's fierce strike crashed onto the crossbar.
Yet it was Lens who regained the advantage in the 73rd minute when Said headed home at the near post from Sotoca's cross.