Keylor Navas, Sergio Ramos, Danilo Pereira and Leonardo Paredes started ahead of Gianluigi Donnarumma, Presnel Kimpembe, Georginio Wijnaldum and Ander Herrera in the PSG line-up.
Mauricio Pochettino's side had a chance to go ahead atfer two minutes from a cutback on the left-wing by Kylian Mbappe, but he scooped narrowly beyond the far post.
Reims continued to hold the Parisans at bay a little over the midway mark and allowed Pereira to head a first-time cross over the intended target with the defence left scrambling.
The breakthrough from the table-toppers arrived in the final minute of the half when Marco Verratti helped Mauro Icardi's blocked shot in off the frame of the woodwork.
There was activity from the visitors' dugout as Dion Lopy and Moreto Cassama entered the field of play, with the visitors looking to get back on level terms.
However, the Parisans increased their advantage with on 62 minutes played when a loose ball in the area from a blocked attempt found Ramos, who needed no second invitation.
As the host introduced Lionel Messi for Angel Di Maria, they added a third goal after five minutes through an own-goal from Wout Faes who deflected a teasing ball into his own net.
Reims' woes were compounded inside the last 15 minutes as Pereira received a telling pass from Mbappe to fire into the back of the net to round off a big win for the home side.