A late equaliser from Steven Naismith earned Kilmarnock a replay in the fourth round of the Scottish Cup.
Wyness headed Hearts into the lead
The Edinburgh side opened the scoring after 16 minutes, when Dennis Wyness headed home a Robbie Neilson cross.
Colin Nish levelled the scores nine minutes later, when he thumped home Alan Johnton's low cross into the penalty area.
Lee Miller put Hearts into the lead just before the break, before Naismith levelled the scores at the death.
Hearts started positively and almost took an early lead when Saulius Mikoliunas squared the ball into the path of Dennis Wyness a few yards out.
Only the quick interception of David Lilley prevented the striker from scoring.
The Tynecastle side took the lead on 16 minutes, when Robbie Neilson's cross into the box was met by Wyness and he left goalkeeper Alan Combe with no chance when he nodded home from six yards.
Only the woodwork denied Hearts a second a few minutes later. Mikoliunaus threaded the ball through to Wyness and he produced a curling effort which smacked off the
Combe managed to kick the ball out of harm's way despite being on the
ground before Liam Fontaine hooked the ball to safety.
Kilmarnock took advantage of poor defending to draw level after 25 minutes.
Allan Johnston's corner from the right found Nish unmarked on the six-yard line and all that was required was to nod home.
Hearts immediately set about trying to re-claim the advantage.
Lee Miller punted into the crowded box and the ball broke to Stephen Simmons who
unleashed a 20-yard drive but the effort fell wide.
Andy Webster then played the ball through to Hartley and he was only denied by
The Kilmarnock goalkeeper was called into action a couple of minutes later and his save was as impressive as Jamie McAllister's thunderous shot.
Hearts found the back of the net just before the whistle, when Hartley embarked on a mazy run before releasing Miller into the box and he left Combe with no chance with a powerful point-blank shot.
Kilmarnock were unfortunate not to draw level again soon after the restart.
Leven sent an inviting corner into the box but Lilley was just off target with the header.
If the last 15 minutes were nail-biting stuff for Hearts then it was largely down to the heroics of Combe who was pulling out all the stops to keep his side in with a chance.
This time it was Wyness who fancied a shot at goal but he was no match for the
keeper who dived to his right to punch clear at the near post.
Instead Hearts were hit with the sucker-punch when Kilmarnock grabbed the
equaliser in the last minute.
A Combe free-kick was headed by Boyd into the path of Naismith who sent a right-footed drive past goalkeeper Craig Gordon to set up a replay on 16 February.
Hearts: Gordon, Neilson, Pressley, Webster, Wallace,
Mikoliunas (Hamill 74), Simmons (MacFarlane 83), Hartley,
McAllister, Wyness (Burchill 78), Miller.
Subs Not Used: Moilanen, Thorarinsson.
Booked: McAllister, Pressley, Hartley.
Goals: Wyness 16, Miller 45.
Kilmarnock: Combe, Ford, Lilley, Fontaine, Hay, Johnston,
McDonald, Locke (Naismith 62), Leven, Nish (Boyd 38),
Invincibile (Murray 62).
Subs Not Used: Smith, Fowler.
Booked: Lilley, Johnston, Leven.
Goals: Nish 25, Naismith 89.
Ref: J Rowbotham