The first chance went the way of PSG, as Mbappe squared the ball looking for Pablo Sarabia, but a defender could only poke the ball to Fabian Ruiz, whose shot forced a stunning save from Yehvann Diouf.
Quick to respond, Reims had a chance of their own midway through the first half, as a loose ball fell to Dion Lopy on the edge of the box, before he struck a volley narrowly over the bar.
PSG reasserted themselves, and had a golden chance to take the lead, when Carlos Soler slipped Mbappé through one on one with the keeper inside the box, but his shot was comfortably saved by Diouf.
The Parisians then worked a second chance from the rebound, but Nordi Mukiele fired over the bar. In an increasingly end-to-end first half, Reims then went storming down the field and almost took the lead themselves, when Marshall Munetsi forced a good save from Gianluigi Donnarumma from close range.
Reims were now proving themselves to be no pushover, and the steep pre-match odds against them shortened further still just before the break, when PSG were reduced to ten men after Ramos was dismissed for dissent.
With a numerical advantage, Reims went close just after the break, as Arber Zeneli sent a powerful low shot towards the near bottom corner, but Donnarumma made a good save to keep it out.
Despite PSG having an off-night, they nearly snatched victory in the dying minutes, when Mbappe crossed the ball in for Danilo Pereira, but the Portuguese defender couldn't keep his header down and sent his effort over the bar.
A good chance went begging for the Parisians, as Neymar found himself through on goal but the Brazilian failed to hit the target with a low effort.
Reims managed to hold on and gained a well-earned point against the champions, as they rose to 14th in the league - albeit at the cost of staying winless at home this campaign.
PSG remain top, but they will know what an opportunity missed this was, having witnessed closest contenders Marseille lose at home to Ajaccio earlier in one of the season’s great shocks.
Flashscore Man of the Match: Yunis Abdelhamid (Reims)
