Lyle Taylor, making his second appearance after joining from Sheffield United on loan, scored his first goal for the club before Aaron Taylor-Sinclair added a second with a header before the interval.
The win for the Jags sees Alan Archibald's side leap-frog Ross County into 10th place. The writing seems to be on the wall for Hearts, however, after they were left 19 points adrift of County.
The only blot on an otherwise flawless afternoon for Thistle was the sending off of Stuart Bannigan for two yellow cards seven minutes from time.
The home side were first to threaten after seven minutes when Callum Paterson headed Kevin McHattie's corner straight at Scott Fox but the goalkeeper spilled the ball. Ryan Stevenson tried to get on to the redound but Fox eventually gained possession.
Steven Lawless responded with an effort for the visitors although his first time left-footed volley from a Taylor-Sinclair cross was straight at Jamie MacDonald.
A free-kick 25 yards from goal then allowed Taylor-Sinclair to test MacDonald, who got across well to his low drive.
The away side stormed ahead after 14 minutes through Taylor. Gabriel Piccolo's long ball was flicked on by Kallum Higginbotham and Taylor held off the challenge of Dylan McGowan to blast a shot in off MacDonald from close range.
The home fans were growing restless as they watched their team struggle to conjure up any meaningful chances. Brad McKay rose high in the box six minutes before the break but he headed McHattie's corner over.
Partick doubled their lead a minute later as Hearts' defensive frailties were again exposed. Higginbotham's corner was met by Taylor-Sinclair and he bulleted a header into the corner of the net.
Hearts tweaked their formation at the interval but Partick came at their hosts again immediately after the restart and MacDonald pulled off a smart save at his near post to deny Taylor from a tight angle.
Hearts defender McKay then powered a header over the bar after connecting with McHattie's inswinging free-kick.
The next chance fell the home side's way too but Callum Tapping's left-footed drive crashed off the bar after taking a slight deflection off Piccolo.
Both teams made changes as Jags attacker Higginbotham was replaced by Christie Elliott, while Hearts introduced Dale Carrick and Billy King for Paterson and David Smith.
Carrick linked with Jordan McGhee at the goal line to allow the latter to cross but Piccolo made a timely interception at the front post with Ryan Stevenson ready to pounce.
Partick played out the final minutes with 10 men, but with few alarms, after midfielder Bannigan collected a second yellow card within four minutes for a late tackle on McHattie.