A stunning goal by Kallum Higginbotham just six minutes from time looked to have given Partick the points, but immediate responses by Hamilton substitutes Tony Andreu and Jason Scotland saw the Lanarkshire men head back along the M74 with all three points.
The win lifts Hamilton on to nine points from four games, while Partick remain on four points from three games after suffering their first defeat.
Hamilton were first to threaten, and should have opened the scoring in the third minute as a long ball from the back was helped on by Mickael Antoine-Curier and then Dougie Imrie to send Louis Longridge scampering in behind the Thistle backline.
However, with defenders getting back to him, Longridge could not get enough on his attempt to lift it over Paul Gallacher, and the Thistle keeper managed to get his left hand to the ball to push it wide.
The visitors were pressing the ball well, and their physical approach in the early stages was preventing Thistle settling into any sort of passing rhythm. They continued to threaten, and only a great last-ditch block prevented Antoine-Curier from opening the scoring after he had been sent clear by by Darian MacKinnon's clever ball over the top.
Eventually the home side came to life after half an hour, and they really should have taken the lead when a long ball from Gallacher found Stephen O'Donnell in acres of space on the right. With just Ziggy Gordon back for Hamilton, O'Donnell raced into the area and had Steven Lawless available square for a tap-in, but the Thistle right-back telegraphed his pass allowing Gordon to make a great interception.
The home side then had two more glorious chances within a minute of each other.
First, a long ball over the top by Dale Keenan put Ryan Stevenson through on Michael McGovern, but a heavy touch by the Thistle frontman allowed the Accies keeper to narrow the angle and make the block. Moments later, Stevenson turned provider to dink a nice ball through to Gary Fraser, who dragged his shot agonisingly wide of McGovern's right-hand post from the edge of the area.
Thistle started the second half in a similarly bright fashion, and a lovely move down the left saw Higginbotham hit the by-line and pull the ball back to the waiting Lawless, whose low effort from near the penalty spot was tipped around the post by McGovern.
The match then went through a scrappy spell with neither side holding on to the ball particularly well or creating any clear-cut chances.
Referee Kevin Clancy, who had infuriated the home support by giving a series of contentious fouls in Hamilton's favour, then angered the Hamilton fans by waving away a penalty appeal after Longridge had claimed that O'Donnell tugged his shirt in the area.
The malaise that had settled on the game was finally broken when a lovely exchange between Crawford and Hamilton substitute Scotland sent the former through on the Thistle goal, but a fantastic last-ditch sliding intervention from Conrad Balatoni saved the home side.
Moments later, a poor free-kick from Fraser allowed Hamilton to break with Danny Redmond running clear down the left and squaring to Crawford who was unmarked in the area. As Gallacher dived to his left, Crawford sent the ball the other way only to be thwarted by the trailing foot of the keeper as he somehow helped the ball wide.
Just as Hamilton looked the more likely to score, Higginbotham, who had been quiet throughout, produced a moment of sublime quality to break the deadlock for Thistle. The winger received the ball 25 yards out and arrowed a thunderous effort into McGovern's top left-hand corner after 84 minutes.
Remarkably, Hamilton hit straight back a minute later, with Crawford playing a lovely reverse ball through the home defence to find Andreu in space, and the substitute made no mistake as he finished high past Gallacher for an immediate equaliser.
Accies were not finished there, and a slip by Balatoni allowed Scotland to race through, the striker making no mistake to finish low past Gallacher to claim victory in the final minute.