Steven Pressley's fourth goal of the season salvaged a valuable point for Hearts as the Tynecastle side ensured they made it to the split in the third place.
Despite dominating for much of the game, Hearts were stunned when Jamie Mitchell headed Partick ahead in the 73rd minute. But the Hearts skipper, returning to the side after missing out last week with an ankle injury, struck just six minutes later to rescue his side.
Scott Severin fired an ambitious 35-yard drive over in the opening minute as Hearts dominated from the outset and could have gone ahead just two minutes later when Steven Boyack sent over a corner from the right and only a goal-line clearance from David Lilley denied Mark de Vries.
Gerry Britton headed over the bar after 14 minutes as Partick finally threatened the Hearts goal but the Hearts pressure continued and Robbie Neilson volleyed over from just outside the area after 20 minutes.
A minute later Steven Craigan did just enough to put de Vries off as the Dutchman fired wide.
Alex Burns came close for the home side after 32 minutes, but Scott Severin was just bale to deflect his low shot behind for a corner.
Lilley was booked after 39 minutes for a late tackle on Austin McCann.
Alex Burns fired a 49th minute free-kick over for Partick, but it was Hearts who continued to dominate with de Vries and Kirk both forcing saves out of Kenny Arthur.
Hearts replaced Jean-Louis Valois with Neil McFarlane after 67 minutes, but it was the introduction of Martin Hardie for Britton that made the biggest difference.
After 73 minutes, Hardie fired in a cross from the right and, although Tepi Moilanen got his hands to Mitchell's downward header, the Finn could not prevent the ball squirming over the line.
Stunned by going behind, Hearts were soon back on the offensive and equalised in the 79th minute.
Stamp swung in a corner, McFarlane provided the head flick at the near post and Pressley turned it past Arthur from close range.