Zlatan Ibrahimovic almost gave the home side the lead inside the opening two minutes, but his long-range strike bounced back off the post.
The visitors also made an attacking start as Mustapha Yatabare tried to force the ball in moments later, but his effort went just high.
The reigning French champions continued to create the better of the chances throughout the game, with Ezequiel Lavezzi, Ibrahimovic and Edinson Cavani all coming close to breaking the deadlock in the first half.
It looked like Guingamp, who had not had a shot on target, would hold onto take a point, but Adrien Rabiot was able to give the home side the lead.
Ibrahimovic slotted home a second moments later following a Gregory van der Wiel break from the re-start to secure to win for PSG.