- Przemyslaw Frankowski (40' Pen)
- Seko Fofana (55')
- Kevin Danso (19')
- Folarin Balogun (23' Pen)
The result put second-placed Lens on 75 points with three games left, three behind leaders Paris St Germain, who take on AC Ajaccio on Saturday, and five ahead of third-placed Marseille, who host Angers on Sunday.
The top two teams qualify for the group phase of the Champions League while the third-placed side will play in the third qualifying round.
"What's happening this season is magical. We knew we'd have chances even when were down to 10 men," said Lens midfielder Florian Sotoca.
Reims went ahead on 23 minutes after being awarded a penalty when Danso was shown a straight red card for pushing Marshall Munetsi in the box.
Balogun coolly slotted the spot kick past Brice Samba to give his team an early lead.
Against the odds, Fofana gave the hosts the advantage 10 minutes into the second half with a superb low shot from just inside the box after being set up by Deiver Machado.
Lens finished in a 5-3-1 formation and hung on for dear life until the final whistle.
- Jeremie Pignard