The Ligue 1 title race will go to the final day after leaders Lille were held by Saint-Etienne, allowing Paris St-Germain to close the gap to one point.
Lille would have claimed the title had they bettered PSG’s result – but they had to settle for a goalless draw.
PSG never looked like slipping up as Reims had Yunis Abdelhamid sent off after 10 minutes and both Neymar and Kylian Mbappe scored before half-time.
Marquinhos and Moise Kean completed a comfortable win for the hosts.
Lille, who struck the post in the closing stages, are away to mid-table Angers and PSG visit 16th-placed Brest in their final league games next Sunday.
Monaco, who face Lens in their last fixture, also remain in the title picture, three points behind Lille, following their 2-1 win over Rennes.
In a dominant first half, Neymar’s 13th-minute penalty into the bottom corner put Mauricio Pochettino’s reigning champions ahead after Abdelhamid was dismissed for handling Mbappe’s shot.
Mbappe then scored his 40th goal in all competitions in 2020-21 – and 26th in Ligue 1 – when he pounced on a defensive mistake.
Marquinhos headed in Neymar’s corner after 68 minutes and substitute Kean scored on the turn in the closing stages.