The visitors started the match the brighter of the two teams and could have taken the lead as early as the fifth minute.
A minute later Sirigu was called into action again, as he denied Diego with a brilliant save.
Reims continued their domination at Parc des Princes with Gaetan Courtet shooting just inches over the PSG crossbar in the 15th minute.
Then Diego came close again for the visitors with a darting run down the right side.
Reims then wasted a glorious chance to take the lead. Gregory van der Wiel was adjudged to have handled the ball inside his own penalty box, but Diego saw his subsequent spot kick saved by Sirigu.
Jeremy Menez was unlucky not to have scored on 63 minutes when his powerful effort rattled the Reims post.
Two minutes later PSG did go in front, as Gameiro headed home past Agassa Kossi from close range.
Reims could have equalised on 76 minutes had Courtet kept his cool from close range, and then Julien Toudic's audacious acrobatic effort came off the PSG crossbar.
Menez went close twice in the space of a minute later on, as Carlo Ancelotti's men had to settle for a 1-0 victory.