Algeria forward Benzia, who turned professional at Lyon before joining Lille in 2015, scored in each half as the northerners pulled away from the relegation zone.
The result left Lyon, who reduced the arrears through Alexandre Lacazette, in fourth place with 37 points from 21 matches, 11 behind leaders Monaco, who visit champions Paris St Germain on Sunday.
Lille have 26 points and now lie five points above the drop zone.
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The hosts got off to a good start, with new signing Memphis Depay being a constant threat to the Lille defence. Mathieu Valbuena was in great shape, too, and saw his free kick hit the bar in the ninth minute.
Lyon, however, fell behind seven minutes before the interval when Benzia's low shot took a slight deflection off Mapou Yanga- Mbiwa and went past Anthony Lopes.
In the 71st minute, Benjamin Cornet's cross was deflected by Lille keeper Vincent Enyeama into the path of Valbuema, but the France international's shot from close range again crashed onto the bar.
OL pushed but Benzia doubled the advantage when he converted a penalty in the 80th minute after Sebastien Corchia had been brought down.
Lyon pulled a goal back as France striker Lacazette scored his 18th league goal with a penalty four minutes from time.
Lacazette came close to equalising two minutes later but his right-footed effort whizzed just past the post.
(Reporting by Julien Pretot, editing by Pritha Sarkar)
