The Uruguayan struck just before the interval before two own goals from Aissa Mandi put the reigning champions on the brink of defending their Ligue 1 crown
The Uruguayan struck shortly before half-time before two second-half own goals from Aissa Mandi sealed maximum points for Laurent Blanc's men.
Victory over Hubert Fournier's side takes the capital club 16 points clear of Monaco, who host Nantes on Sunday, and defeat for Claudio Ranieri's side will give PSG the chance to wrap up their second successive title next week at Olympique Lyonnais.
PSG used the opportunity to rest several key players ahead of Tuesday's Champions League quarter-final second leg at Chelsea.
Though 3-1 up from the first leg, the likes of Thiago Motta, Ezequiel Lavezzi and Blaise Matuidi were all benched ahead of the trip to west London.
Below-par in the week, Cavani was razor-sharp throughout the first half and went close 14 minutes in after racing onto Adrien Rabiot's pass, but Mickael Tacalfred recovered well to deny him.
Reims' attacks were few and far between but Odair Fortes almost caught Salvatore Sirigu out with a long-distance effort.
Visiting goalkeeper Kossi Agassa was perhaps fortunate not to concede a penalty with 10 minutes of the half to go after felling the impressive Lucas Moura, but referee Laurent Duhamel was unmoved.
And PSG's dominance was finally rewarded in the 43rd minute as Cavani slotted home after good work on the right from Gregory van der Wiel.
The first half had seen Blanc's side frustrated, but they were quick to strike again after the break.
PSG's left-back Lucas Digne fashioned an opening down the left before the teenager's cross was headed towards goal by Lucas and deflected in by the hapless Mandi.
Cavani had a gilt-edged chance to double his tally 10 minutes into the second period, but he drilled his effort wide, with Jeremy Menez also shooting off-target soon afterwards.
Mandi then passed up a chance to redeem his earlier slip, heading Floyd Ayite's free kick over the crossbar as PSG sat back in hopes of preserving their lead.
Lavezzi emerged from the bench to replace Cavani with 25 minutes to go and saw a penalty appeal waved away after going down under a challenge from Tacalfred.
And with Chelsea on the horizon, PSG easily kept up their winning habit as Mandi inexplicably turned past Agassa for a second time with two minutes to go, securing the hosts an 11th-consecutive victory in all competitions ahead of the trip to London.