After a season of turmoil, Gary Locke's financially-stricken side were left relying on other results to delay their fate for another week, having earned yet another reprieve with their midweek draw against Aberdeen.
They needed to win themselves and hope that St Mirren lost to Motherwell.
But despite Hearts doing their bit, Motherwell failed to do them a favour - with St Mirren snatching a 3-2 victory courtesy of two goals in the last four minutes.
At Firhill, Hearts had shown the type of resilience that has been a belated feature of the last few weeks as Kris Doolan's early opener was cancelled out by Dale Carrick.
Billy King then gave the visitors the advantage just after half-time and a double from Ryan Stevenson sealed the win, with Jordan McMillan's late strike mere consolation for Partick.
But St Mirren had not read the same script and they fought back from two goals down to clinch victory.
Henri Anier and John Sutton both scored to give Motherwell a commanding lead after just 27 minutes, but Steven Thompson's volley before half-time gave the home side hope.
And the comeback was completed in the second half with two goals in as many late minutes coming via Kenny McLean's penalty and Thompson's second.
At the top, champions Celtic recorded an easy 2-0 victory over Dundee United.
Georgios Samaras gave Neil Lennon's side an early lead with a fantastic volley after a free-kick from Kris Commons.
His strike partner Anthony Stokes then doubled the advantage before half-time with a fine finish after a lovely flowing team move.
The loss puts a dent in the hosts' ambitions of European football, although their place in the top six was long ago secured heading into the final round of fixtures before the league's split.
St Johnstone occupy that final top-six spot and cannot be caught, as they warmed up for their Scottish Cup semi-final against Aberdeen next week by staging a comeback to beat Kilmarnock 2-1.
