Hubert Fournier's side slipped to sixth as a result of points picked up by Saint-Etienne, Rennes and Bordeaux earlier in the week and it looked as though they would miss the chance to move back into the European spots.
Corentin Tolisso put the home side ahead after just six minutes when he headed the opening goal following a delivery from Nabil Fekir.
However, Benjamin Moukandjo levelled nine minute before the break when he took advantage of a spilled effort from Prince Oniangue.
Anthony Lopes could not hold on to the strike, with Moukandjo on hand to finish as he became the first player to score in five consecutive Ligue 1 games this season.
Just when it seemed as though Reims were to ensure an impressive away point, Lacazette again showed his lethal touch in the first minute of stoppage time.
After an impressive start to the campaign, the France international had failed to score since his return from the international break last month but Johnny Placide was unable to keep his long-range strike out.
Lacazette's 12th Ligue 1 goal of the season moves Lyon back to third, while Reims remain ninth having lost in the top flight for the first time in eight matches.
