Rennes skipper Hansson deflected into his own net a shot by substitute Nicolas Fauvergue 15 minutes from time after the Lille striker had latched on to a Michel Bastos cross.
Rennes, who had not lost in their last 18 league matches, are fourth in the standings with 37 points from 21 matches, five points adrift of leaders Olympique Lyon, 2-0 winners at Grenoble on Saturday.
Rennes had midfielder Bruno Cheyrou sent off in the 89th minute for a second bookable offence.
Lille, who dominated throughout, are seventh on 35 points but have a game in hand.
Earlier on Sunday a second-half goal from Peguy Luyindula (pictured) earned Paris St Germain a 2-1 home win against lowly Sochaux.
PSG, who were handed a 4-0 thrashing by Girondins Bordeaux last weekend, remain sixth on 36 points, while Sochaux stay third from bottom on 17 points.
At the Parc des Princes, striker Guillaume Hoarau netted his 12th goal of the season when he converted from the spot three minutes into first-half stoppage time following a foul on Jerome Rothen.
But it was not enough to end Sochaux's resilience as Vaclav Sverkos levelled with a fine volley on the turn.
PSG, however, sealed the win shortly after the hour when Luyindula poked the ball home from a Sylvain Armand header.
Elsewhere, Monaco squandered a two-goal lead when goals by Juan Pablo Pino and Alejandro Alonso were cancelled out by Steve Savidan and Benjamin Nivet for a 2-2 draw at Caen.
