St Mirren's victory over Motherwell sealed the Jambos' exit from the top division, despite the 4-2 success at Firhill.
Partick took the lead in the opening stages through Kris Doolan before goals from Dale Carrick and Billy King either side of half-time put Hearts in front.
Ryan Stevenson then hit a fine double to put the seal on a stunning victory for the Jambos despite a late consolation from Jordan McMillan.
Thistle, who remain entrenched in the battle to avoid finishing in the relegation play-off spot, dominated the opening period of the game.
The hosts opened the scoring after just five minutes. A ball over the top from Aaron Taylor-Sinclair should really have been dealt with by the Hearts defence, but as Brad McKay and Dylan McGowan hesitated, Doolan latched on to the ball to race clear and produce a fine left-foot finish past Jamie MacDonald on the half-volley for his ninth of the season.
They almost moved further ahead after 15 minutes. Kallum Higginbotham challenged for a high ball that appeared to come off his arm, but as the Hearts players appealed for a foul, referee Stephen Finnie waved play-on and Higginbotham slid a lovely through-ball into the path of Lyle Taylor, who should have done better than blaze over the bar.
Hearts had rarely been seen as an attacking force in the opening half hour, however a break by Billy King on the left led to the first of a series of corners, one of which almost drew them level.
Kevin McHattie's fine delivery from the right was met in the centre of the box by the head of Scott Robinson, who was only denied by a fine point-blank save from Paul Gallacher.
It was then the turn of the Thistle defence to be caught out by a long ball, as King raced clear of the flat-footed Lee Mair but dragged his right-foot effort tamely wide.
Hearts were gaining in confidence though, and King went closer with a stinging drive that was parried away by Gallacher.
The visitors grabbed the equaliser that their increasing pressure merited on 44 minutes. Again King was involved, making himself a yard of space on the left to clip a ball into the six-yard box where Carrick headed home from close range.
Better was to come for the visiting supporters in the opening stages of the second half.
The Thistle defence could only clear a high ball as far as King who was lurking on the edge of the area. The winger had time to take a touch before unleashing a stunning left-foot effort into the top corner to give his side a 49th-minute lead.
The home side were ragged now, and they fell further behind after 63 minutes.
Thistle had looked vulnerable to crosses into their area all game, and again they were undone as Robinson's corner was glanced across Gallacher into the corner of the net by Stevenson.
Hearts moved 4-1 ahead after 70 minutes, with Stevenson again on the scoresheet.
The ball was gifted to Robinson by Taylor-Sinclair and he drove into the Thistle area before cutting the ball back to Stevenson. With his back to goal, the forward turned his man brilliantly before slotting a left-foot effort into the bottom corner.
Hearts saw out the game despite Jordan McMillan's impressive 88th-minute finish for the home side.
However, it was not enough to save them from the drop - and Partick now face a real battle to avoid the relegation play-off position.