Marseille, who had lost their last two competitive games, now have 28 points from 12 games after Nicolas Nkoulou and Thauvin scored either side of the interval.
Champions Paris St Germain are second on 24 after they beat Lorient 2-1 away on Saturday, while Olympique Lyonnais sit in third one point further back following their 3-1 win at Nice, also on Saturday.
PSG and Marseille face each other at the Parc des Princes next Sunday.
Lens, who played some decent football and equalised through Baptiste Guillaume in the first half, are 17th on 11 points.
“We played against a very good team,” OM defender Rod Fanni told Canal Plus.
“We made some mistakes after opening the scoring and we gave them hope. It was complicated but we managed to snatch three important points.”
Marcelo Bielsa’s team made a good start and went ahead in the 10th minute when Nkoulou found the back of the net with a diving header from Thauvin’s corner.
Lens, however, levelled in the 31st minute as Guillaume, after being set up by Pablo Chavarria, beat Steve Mandanda with a low shot from inside the box.
Thauvin put the home side back in front on the hour, scoring from close range after collecting a pass from Andre-Pierre Gignac.
OM, however, finished the game with 10 men when Romao was sent off in the 75th minute after fouling Wylan Cyprien, collecting his second yellow card of the evening.
Lens pushed hard but OM held firm, with Mandanda denying Yoann Touzghar from close range with a spectacular save in added time.
(Reporting by Julien Pretot; Editing by Mark Meadows)