Gameiro, who had only played 71 minutes in the league this season, scored a first-half double as PSG confirmed they had reached cruising speed after a stuttering start.
Carlo Ancelotti's side are on 15 points and trail arch rivals Marseille, who they travel to next weekend, by three points before the leaders attempt to maintain their perfect start away to Valenciennes on Sunday.
"We were not that good in the second half, we started to get a little bit tired, it's normal," keeper Salvatore Sirigu told Canal Plus. "The good thing today is the result. There is still room for improvement but we keep cool."
PSG, who spent more than 200 million euros on transfers since being bought by Qatar investors last year, were a class apart, dominating possession with a steely midfield marshalled by the impressive Marco Verratti.
Javier Pastore's delicately chipped pass into the path of Gameiro allowed the latter to make it 1-0 with a low shot after 11 minutes. Gameiro doubled the lead 12 minutes from the interval when he latched on to a Maxwell cross from the left.
PSG looked slightly weary after the break but Brazilian centre backs Thiago Silva and Alex made sure Sirigu would be unchallenged until the final whistle.
Gameiro's double made up for Zlatan Ibrahimovic's failure to score for the first time in seven PSG appearances.
PSG have scored 10 goals from their last three games before a couple of important challenges next week as they travel to Porto in the Champions League before the "classic" with Marseille.
Morocco midfielder Younes Belhanda fired home from a Karim Ait Fana pass midway through the second half and Souleymane Camara struck late to give champions Montpellier a 2-0 win at Nancy.
Montpellier's second victory of the season put them on eight points, 10 adrift of Marseille.
Lorient stayed fourth on 13 points after Gilles Sunu's late goal salvaged a 1-1 draw at Evian.
Toulouse were fifth, one point behind, thanks to their 2-0 win at promoted Troyes.
On Sunday, Lyon will have the opportunity to leapfrog PSG into second when they host unbeaten Bordeaux.