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.
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St Mirren climbed out of the relegation play-off spot after a dramatic late turnaround earned them a 3-2 home victory over Motherwell.
Henri Anier and John Sutton took advantage of a St Mirren defence that appeared disorganised and uncomfortable while playing a high line to put Motherwell two ahead inside 27 minutes.
But, with Motherwell missing injured centre-back Shaun Hutchinson, St Mirren looked dangerous at corners and Steven Thompson converted one just before the break to give the Buddies hope.
They pressed in the early stages of the second half but Motherwell had chances on the break and appeared to have withstood the pressure.
However, stand-in referee Iain Brines awarded the hosts a controversial penalty for handball by Stephen McManus in the 86th minute.
McManus had blocked Thompson's header at point-blank range but Brines, after some hesitation, decided it was deliberate handball despite the Motherwell defender's protests.
Kenny McLean converted from the spot and Thompson stunned the visitors when he turned and fired home from close range a minute later.
Defensive duo Frazer Wright and Steven Anderson both struck first-half goals as St Johnstone came from behind to beat Kilmarnock 2-1 at Rugby Park.
Robbie Muirhead had given the hosts an early lead but despite a bright start, Killie failed to build on their lead.
That proved costly as they then twice allowed themselves to be breached from dangerous corner deliveries in the final 15 minutes of the first period.
The win was perfect preparation for Saints ahead of next weekend's William Hill Scottish Cup semi-final against Aberdeen, but leaves Allan Johnstone's side now perched just three points above 11th-placed Partick Thistle and the relegation play-off slot.
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