Lille closes in on European bid
Kalou struck in either half, sandwiching a strike by Dimitri Payet as the hosts moved into fourth spot ahead of Nice on goal difference, with Claude Puel's side playing Evian on Sunday.
Defeat leaves Reims five points above Evian, who occupy the third relegation spot with the latter having three games remaining.
Lille almost took an early lead when Payet's corner found Ronnie Rodelin at the far post and his header skimmed the woodwork.
The hosts went ahead in the 20th minute. Rodelin flicked the ball through to Kalou with the former Chelsea player outpacing defender Anthony Weber before dribbling past goalkeeper Kossi Agassa and slotting the ball into an empty net.
It was all Lille as Marvin Martin freed Payet on the right of the area and he raced into the middle and past the attentions of defender Antoine Devaux before curling a left-footed shot which crashed against the bar.
Payet was a constant menace to Reims and his fierce drive forced Agassa to go full stretch to keep the ball out but despite all their domination, Rudi Garcia's side only went in at the break a goal to the good.
They were almost made to pay three minutes after the break as they enjoyed some good fortune when Diego's snap-shot went between goalkeeper Barel Mouko's legs but rolled along the line rather than over it.
Lille heeded the warning and doubled their lead a minute later as Payet got a thoroughly deserved goal. Martin flicked the ball up front towards Payet who raced to the edge of the area and unleashed a fierce shot which flew just under the bar.
Rodelin hit the side netting with a shot before the visitors almost pulled one back when Floyd Ayite's left-footed volley went inches over the bar.
However, victory was confirmed for Lille 13 minutes from time and again Payet was involved, freeing Kalou who raced along the edge of the area and past defender Franck Signorino before he unleashed a sudden low shot to beat Agassa to his left.