Christophe Berra headed the Premiership side into an early lead as the visitors dominated at Firhill.

But Thistle, bottom of Scotland's second tier, salvaged the tie thanks to a second-half Christie Elliott strike.

The replay, to win a last-four date with Inverness Caley Thistle, will take place on Tuesday, 12 March.

Hearts, who exited at the quarter-final stage last season to Motherwell, controlled large chunks of the game with Sean Clare and Uche Ikpeazu going close.

Holders Celtic will take on either Aberdeen or Rangers in the other Hampden semi-final.

Beacon of hope for Thistle

On the face of it, this was a shot at nothing for Thistle. Playing a team from the division above with little pressure from outside of Firhill, the team from the Championship should have gone in to this one with nothing to fear.

However, Gary Caldwell's side were timid in their approach to toppling Craig Levein's Hearts.

Within the first minute Berra turned a header wide in an early warning. Still, they sat deep, allowing their visitors to attack, and they paid the price.

Ben Garuccio's lofted ball into the box caught Thistle napping as Berra outjumped Steven Saunders to thump a header high into the net.

There was little response from Caldwell's side, who failed to step up and try to get back into the match as Hearts coasted towards half-time.

After the break, it was much the same in the opening stages as a large home support tried to urge their side forward.

Instead, their hearts would have been in their mouths as Levein's men went inches from what would have been a decisive second.

A Clare shot was acrobatically tipped on to the frame of the goal from the angle by Conor Hazard. Ikpeazu reacted first to the rebound. He headed the ball in the air, before then diverting his next header on to the bar and over.

With the writing on the wall for Thistle, from nowhere they got the goal that almost took the roof off the Jackie Husband stand.

It came just three minutes after that scare at the other end. Craig Slater drove for the line on the left to swing in a perfect ball across goal. Elliott met it at the back post in what was Thistle's first meaningful chance of the game, smashing in his second goal of the season.

Ikpeazu went down in the box following Gary Harkins' challenge but no penalty was awarded by referee Bobby Madden.

Both sides will need to up their game - analysis

BBC Sport Scotland's Jane Lewis at Firhill

Hearts should have already secured their semi-final place. They were the better team tonight, and while Partick Thistle's goal was well taken, they offered little on the night.

Hearts were guilty too at times, and striker Uche Ikpeazu cut a frustrated figure as he picked up his man-of-the-match bottle of fizz, admitting they should have finished the job.

With Inverness Caledonian Thistle awaiting the winners in the semi-finals, the incentive, as if one was needed, is massive for both teams having avoided Aberdeen, Rangers and Celtic.

Hearts will be overwhelming favourites for the replay on Tuesday week, the Championship basement club will have to show great improvement if they're to progress. Hearts though, on tonight's evidence, will also have to up their game.