A first-half goal from Chris Erskine and a header from Lee Mair put Thistle in the driving seat.
Duncan Watmore hit back for Hibs to give them hope of salvaging something from the game, but man of the match Kallum Higginbotham sealed matters in stoppage time.
The hosts were straight on the offensive from kick-off with Lyle Taylor winning a free-kick on the edge of the Hibernian box, and Kallum Higginbotham firing the resulting low effort straight at Ben Williams.
Hibs then passed up a great opportunity on the break a few minutes later. From a Thistle corner, Jason Cummings broke free on the left but failed to spot James Collins in acres of space through the middle, and by the time the youngster lifted his head to find his strike partner Thistle had men back to cover the danger.
The promising opening to the game made way to a much scrappier passage of play where both sides struggled to retain possession, but Higginbotham burst into life after half an hour to finally give the home crowd something to get excited about.
Operating on the right, the Englishman went on a fine run, cutting inside two Hibs defenders before unleashing a left-footed effort that Williams did well to parry over.
Thistle passed up an even better chance moments later, Higginbotham turning provider on this occasion by cleverly finding Erskine unmarked inside the area.
The on-loan Dundee United man should have done better than tamely sidefoot into the arms of Williams from 12 yards.
He was to make amends, however, by opening the scoring after 43 minutes.
Again, Higginbotham was pivotal to the move, skipping past a couple of attempted tackles before releasing Taylor in the inside-right channel. His cut-back was dummied by Kris Doolan to Erskine, who took a touch before rocketing a left-footed shot high past Williams into the roof of the net.
Hibs had struggled to trouble Paul Gallacher in the first period, but in the opening minute of the second half Cummings did well to find some space in the area before firing in a low effort that the Thistle keeper parried wide.
Partick then had a good opportunity on the counter-attack as Prince Buaben's cross-field pass found Higginbotham with time and space. With men over he elected to run on and shoot himself, but could only fire straight at Williams.
They did not have to wait long to double their lead, however. Taylor was fouled wide on the Thistle left and Higginbotham's inswinging delivery was glanced into the corner of the net by Mair - his first goal for the club - after 59 minutes.
Any notion Thistle had that the game was over was swiftly put to bed, though, as Hibs hit back just three minutes later.
Sam Stanton did well down the left before cutting the ball back to Watmore. The attacker held off a challenge before curling a low effort past Gallacher to bring his side right back into the match.
Stephen O'Donnell almost drew the visitors level by putting through his own net, Gallacher having to make a smart save with his legs after Hibs substitute Paul Heffernan's low cross had cannoned off the right-back as he tried to clear.
A series of Hibs corners in the last 10 minutes tested Thistle's resolve, but Higginbotham broke clear in the 92nd minute and kept his composure to side-step Michael Nelson and Williams before finishing low into the corner to seal the victory.