Ronny Rodelin gave Rene Girard's men the lead in the 47th minute, but Franck Beria was sent off for a second bookable offence five minutes later.
Lowly Valenciennes pushed for an equaliser as they tried to make the most of their one-man advantage, but Lille held on to their lead and are now one point behind PSG, who play Lyon on Sunday.
Third-placed Monaco were also victorious, as they picked up a 2-0 win over Rennes.
James Rodriguez opened the scoring in the 19th minute before Anthony Martial doubled the advantage a minute before the break.
The victory leaves Claudio Ranieri's men two points short of PSG, while Rennes are 12th.
Saint-Etienne recorded back-to-back victories for the first time since early September as they claimed a convincing 4-0 triumph over Reims.
Christophe Galtier's side - whose fans were banned from away games for the rest of 2013 this week following last weekend's crowd trouble at Nice - scored goals in the second half from Moustapha Sall, Mevlut Erding and a Loic Perrin brace to seal all three points.
Seventh-placed Guingamp closed the gap on Nantes above them as they edged to a 1-0 victory in a clash between the sides, with Younousse Sankhare scoring the only goal of the encounter just after the hour mark.
Elsewhere, rock-bottom Sochaux were thrashed 5-1 by Toulouse, despite having taken an eighth-minute lead, while Lorient leapfrogged Nice with a 3-0 home victory.
