The result means PSG will finish the weekend top of Ligue 1 on 14 points ahead of Rennes, who drew with Lille on Friday, on 13 while Caen are third on 12 after a 2-1 win over Montpellier.
All eyes, however, will be on Marseille on Sunday night as they host Lyon in the pick of the weekend games.
At Reims, the two goals came within a minute of each other as home defender Jordan Saibatcheu took advantage of some hapless defending to give his side an 83rd minute lead, which would have been enough to carry his side level with the Parisians at the top.
But PSG responded in style as Argentine playmaker Javier Pastore played a peach of a through-ball and Cavani rushed into the area to clip a slick shot past goalkeeper Kossi Agassa.
It was his fifth league strike of the season.
"It would have been an injustice if we had lost this match, but we're disappointed with the result," said PSG coach Laurent Blanc.
"Because we should also have scored more goals. We just were not nasty enough, in the good sense of the word."
A badly misfiring Zlatan Ibrahimovic had missed a sitter on 62 minutes, fluffing a straightforward header with Agassa sat on the floor and the goal entirely at his mercy, the Swede inexplicably nodding an easy chance wide.
"I thought I played alright, but I have to admit I really did miss a very easy chance indeed," the giant Swedish striker admitted.
That was the moment Blanc went for broke and brought on Angel Di Maria, Cavani and Blaise Matuidi, who had been left on the bench after the midweek 2-0 win over Malmo in the Champions League.
Reims handler Olivier Guegan expressed frustration at his side's inability to hold on to their hard-earned lead.
