The result was tinged with fortune though, after Carlo Ancelotti's men had seen Diego miss from the spot for their opponents earlier in the match.
PSG are now unbeaten in nine league matches and move level on points with leaders Marseille, who take on Troyes on Sunday.
Newcomers Reims have been something of a revelation so far this season and there was no sign of fear against their illustrious opponents, with Diego's early strike from 25 yards having to be palmed away by goalkeeper Salvatore Sirigu.
PSG responded with Zlatan Ibrahimovic teeing up Maxwell, although the Brazilian defender could only fire straight at Reims keeper Agassa Kossi.
The home side then saw a Gameiro strike cleared off the line by Aissa Mandi, and they made life even more difficult for themselves six minutes before the interval when Gregory van der Wiel was penalised for a handball in the area.
However, Sirigu was equal to Diego's spot-kick with a fine save low to his left.
It was a huge let-off for PSG and they tried to assert their authority after the interval.
But if luck had been on their side in the first half, it seemed to be against them now as Blaise Matuidi struck the crossbar with a 55th-minute volley before the same player smashed a shot on to the post nine minutes later.
Gameiro came to the rescue after 64 minutes though, with Maxwell delivering a superb ball to the far post which the former Barcelona player headed in.
Reims came under pressure for the rest of the half and only two fine saves from Kossi prevented Ibrahimovic from adding gloss to the scoreline.