Georgios Samaras headed the champions in front in the 33rd minute but Thistle were rewarded for a period of sustained pressure when Kris Doolan shot them level 23 minutes from time.
However, their celebrations were cut short when substitute Amido Balde made the most of an error from Sean Welsh to shoot beyond the excellent Scott Fox eight minutes later.
Fox, who had a three-year spell with the Hoops between 2007-2010, kept the visitors at bay with fine first-half saves from Teemu Pukki (twice) and the impressive Anthony Stokes.
But he was left with no chance when a completely unmarked Samaras headed home the opener - his 70th for the club - from a pinpoint Emilio Izaguirre corner.
And two minutes later central defender Virgil Van Dyk found himself similarly isolated in the box but his header sailed wide of Fox's goal.
After the break Celtic defender Efe Ambrose gifted the ball straight to Stuart Bannigan but the midfielder's 30-yard effort was easily dealt with by Fraser Forster.
And as Thistle continued to threaten, another error from Ambrose allowed wing-back Christie Elliott a sight of goal but a timely tackle from Izaguirre cleared the danger.
But the Jags soon found themselves level when Doolan, who had earlier rattled Forster's crossbar, poked the ball beyond the keeper's outstretched hands after fine work by Kallum Higginbotham.
Thistle were visibly buoyed by the goal and Higginbotham missed a chance to put them ahead shortly before the game's turning point.
With play bogged down in midfield and little danger to either side, Welsh was dispossessed by Izaguirre who quickly found Balde unmarked on the halfway line.
And the Portuguese striker strolled the length of the Thistle half before slotting the ball beyond the advancing Fox to secure all three points for the Hoops, who remained unbeaten for the first quarter of the campaign for the first time since Martin O'Neill's side in 2003-2004.
Izaguirre was later forced off with a head injury and Celtic, who had used all three substitutes, played out the closing stages with 10 men after Samaras left the field with a deep gash to his knee.