The home side made a whirlwind start to the match and Shunsuke Nakamura almost fired them in front inside the opening 20 seconds.
The Japanese midfielder cut inside and fired in a powerful left-foot effort that Caley keeper Mark Brown did well to save.
But it was the visitors who should have netted the opening goal a few minutes later. Bobo Balde failed to clear, gifting Thistle frontman Graham Bayne an excellent opportunity to net. But he lifted his effort over the bar when it appeared easier to poke the ball low past Artur Boruc.
Another breathtaking save from Brown denied Celtic midway through the first half. Maciej Zurawski slid the ball through to Nakamura, but Brown stuck out his left hand and parried the ball to safety.
Celtic lost the services of Stilian Petrov on the half-hour mark when he picked up a hamstring strain, but five minutes later, Stephen McManus put Celtic in front with a fine looping header that went in off the underside of the crossbar.
Celtic should have doubled their advantage five minutes after the break, but John Hartson missed a sitter, knocking wide of target from Mark Wilson's cross.
The SPL leaders made sure of the points 11 minutes from the end when Shaun Maloney netted a fantastic curling free-kick from the edge of the area.
But a late howler by Boruc took the gloss off the victory as he gifted Caley an injury time consolation goal, allowing a low Richie Hart effort to squirm through his grasp.