Jonathan David sends Lille into Champions League spots
A miscued backpass from Reims captain Abdelhamid allowed Lille's Canadian striker to race through before slotting past Yehvann Diouf just before the hour, securing a 1-0 victory.
The win allowed Paulo Fonseca and his team to bounce back from a 3-1 defeat at Toulouse last weekend and provisionally leapfrog Nice into fourth, the final Champions League spot in the table.
The Portuguese coach was pleased with the "tactically perfect match" that his charges played out in Reims to earn their first away league win since November.
Regarding this poor away form, Fonseca said: "The problem was that we were playing against teams that weren't very strong. I've spoken to the players about it, and we need to change this mentality."
Lille went into the break goalless against their eighth-placed hosts but did create the best chance of a close-fought first period when only a fine double save by Diouf kept the sides level.
The Reims stopper did not cover himself in glory when he pushed Edon Zhegrova's angled strike straight to the feet of David, but he reacted superbly to foil the striker before Thibault De Smet hacked clear with the goal gaping.
David's next big chance came on 56 minutes and this time he was clinical when the last defender fluffed his pass, intercepting and sweeping home past the stranded 'keeper for the only goal.
The home side came to life as the clock ticked down but Lucas Chevalier, in goal, and the Lille defence withstood the tide and held on to their clean sheet.
Later on Saturday, bottom-of-the-table Clermont host Jean-Louis Gasset's Marseille, who can move up three places with a win.