The Sweden star struck just minutes after teenager Adrien Rabiot had given the Ligue 1 champions the lead in the dying moments at Parc des Princes
The French champions appeared to be heading for a stalemate against their spirited opponents after 90 minutes of frustrating football for the home faithful, until the 18-year-old bundled home a rebound in injury time before the Swede settled matters just before the final whistle.
PSG came into the game looking for its first home win of the season and almost snatched the perfect start as Ibrahimovic curled a 25-yard free-kick onto the post just two minutes in.
The tone was set for the early exchanges, with the hosts dominating much of the possession in midfield, but they struggled to unlock a determined Guingamp defense. The visitors themselves were a threat on the break as Claudio Beauvue and Sadio Diallo both went close.
Ten minutes before the break, the hosts created a flurry of chances, with Thiago Silva’s header being denied by Mamadou Samassa in the six-yard box.
Moments later it was the post to come to the visitors' rescue, with Thiago Silva once again foiled.
PSG began brightly after the break, with Samassa coming to the rescue of his team again to parry away a low Cavani effort after a well-worked corner.
But the three-pronged attack of Ezequiel Lavezzi, Ibrahimovic and Cavani continued to be frustrated by a dogged Guingamp defense, with the Swede enduring a particularly difficult afternoon, skying an effort from 25 yards just after the hour mark.
PSG continued to knock on the door and nearly broke the deadlock in spectacular circumstances when Cavani sent a powerful effort narrowly wide on 67 minutes, before setting up Ibrahimovic just a minute later, with the Swede also off target.
It looked as though the visitors would hold on for a draw, until a whipped free-kick was met by Alex, whose header was parried straight to substitute Rabiot, who applied a calm finish with his knee from close range.
And just two minutes later the win was sealed, when Ibrahimovic latched onto a long ball to round Samassa and roll the ball into an empty net.