The France midfielder produced a composed finish shortly before the hour mark in Marrakech.
Both sides had been guilty of wasting presentable opportunities before that, but a combination of profligate finishing and good goalkeeping kept the game scoreless until Cabaye's intervention.
Mauro Icardi missed two chances for Inter in the first half, before PSG star Zlatan Ibrahimovic - facing one of his former clubs - brought a fine save out of Samir Handanovic shortly after the restart.
Both sides will now return to domestic competition in the new year, with reigning Ligue 1 champions PSG set to take on Montpellier in the Coupe de France on Monday and Inter due to take on Serie A leaders Juventus in a week's time.
Following a quiet start, PSG goalkeeper Nicolas Douchez was forced to rush from his line to deny Icardi's effort with his legs in the 28th minute.
Douchez's opposite number Handanovic was called into action 10 minutes later, keeping out Adrien Rabiot's effort from distance and then getting to his feet to parry Blaise Matuidi's rebound.
Icardi had another opportunity to open the scoring two minutes prior to the interval when he was played in by Mateo Kovacic's superb throughball.
But, after this time lifting the ball over the advancing Douchez, he was only able to hit the side-netting.
Ibrahimovic ought to have put PSG in the lead early in the second half but his close-range effort was well kept out by Handanovic.
The Inter keeper was then replaced by Juan Pablo Carrizo, who had to palm away Matuidi's deflected cross as it threatened to drop in at the far post.
PSG were rewarded for their strong start to the second period when Cabaye swept home the loose ball after Inter failed to clear Gregory van der Wiel's low delivery into the box.
