Chris Erskine and Lee Mair fired the hosts into a two-goal lead, Duncan Watmore pulled one back for the visitors, before Kallum Higginbotham sealed the points in second-half injury-time.
Partick broke the deadlock two minutes before half-time when Lyle Taylor fed Erskine who clinically found the top left-hand corner of the net from 15 yards.
And it was no less than Thistle deserved with both Higginbotham and Erskine offering plenty of threat during the opening 45 minutes.
Hibs, who had needed 38 minutes to create a decent strike on goal when James Collins fired inches wide of the left post, made a strong start to the second half by conjuring up a couple of decent efforts inside the opening two minutes.
First, a low shot from Jason Cummings was saved by keeper Paul Gallagher before Michael Nelson missed a close-range header as he nodded the ball over the bar.
But with an hour played, Partick extended their lead through Mair whose header found the bottom right-hand corner from Higginbotham's free-kick.
However, Hibs hit back less than two minutes later when Samuel Stanton laid the ball back to Watmore whose low shot sneaked just inside Gallagher's left-hand post.
As Hibs chased an equaliser Nelson nodded narrowly wide while, at the other end, Aaron Taylor-Sinclair came close to grabbing a third for Partick.
And with 91 minutes on the clock, man-of-the-match Higginbotham eased the home side's nerves as he slotted home from 12 yards, after latching on to Christie Elliott's pass.