Terrier struck four minutes from full-time to put Lyon on 56 points from 30 games, one point behind second-placed Lille who travel to Nantes on Sunday, and nine ahead of fourth-placed Marseille who host Angers on Saturday.
Runaway leaders Paris Saint-Germain, who travel to Toulouse on Sunday, have 77 points from 28 matches.
Lyon president Jean-Michel Aulas is expected to say on Tuesday whether he will extend Genesio's contract beyond the end of the season.
French media have reported that he will keep hold of the 52-year-old if the team finish in the top three, with third place securing a spot in the UEFA Champions League qualifiers.
Lyon were largely toothless for most of the game, although Nabil Fekir's first-half effort hit the woodwork.
They were, however, rewarded for their domination in the 86th minute when second-half substitute Terrier latched onto Leo Dubois's cross at the near post to give Lyon all three points.
The result left Rennes in eighth place on 41 points.
