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Sean Clare's penalty was his fourth goal in five games

Sean Clare's second-half penalty put Premiership strugglers Hearts into the quarter-finals of the Scottish Cup as they edged out League One side Falkirk.

Clare netted his fourth in five games after Michael Doyle fouled Liam Boyce.

Falkirk hit the frame of the goal three times in response - and twice within a minute through Declan McManus - but could not find an equaliser.

Daniel Stendel's Hearts go into Sunday's draw, which takes place after Clyde's tie against Celtic.

Hearts get job done in testing conditions

The arrival of Storm Ciara during the day ensured the players were in for a difficult evening.

Such was the wind that in the opening two minutes, Hearts' pair Andy Irving and Ben Garuccio both played balls forward for their strikers to chase that ended up rolling off the end of the pitch.

In the opening 30 minutes, Clare and Falkirk's Paul Dixon and Gary Miller were all booked by referee John Beaton as players struggled to cope with the slippery conditions on the Astroturf pitch.

Hearts, though, began the better side and Garuccio did extremely well to find space down the left but his cross into the box evaded everyone.

But perhaps lacking in confidence from their toils in the league, even the shortest of passes by Hearts quickly began going astray, which gave the hosts a boost as they began to make an impact on the game.

There was, however, a distinct lack of quality with neither team able to grasp control.

Falkirk were given a clear sight of goal when Clevid Dikamona misjudged a long ball forward by Dixon to give Josh Todd a clear run through but, as the Hearts defence raced back, the Falkirk striker blasted high over the crossbar.

Hearts' first serious attempt on goal came just four minutes before the break but Robbie Mutch in the home goal dived low to his left to deny Boyce.

And the game finally burst into life five minutes into the second half as Boyce chased a long ball inside the box and was bundled to the ground by Doyle's clumsy challenge.

Referee Beaton pointed to the spot and Clare slotted the ball low into the corner to continue his excellent recent form.

Falkirk's response was excellent with McManus twice denied an equaliser by the same post, as the home fans began to roar on their team.

Miller was next to try his luck as Falkirk continued to push forward but his terrific shot from 25 yards came back off the crossbar with Hearts' goalkeeper Joel Pereira well beaten.

Hearts captain Steven Naismith took a knock on his right knee and was replaced on the hour mark by Jamie Walker, which will be a concern for Stendel as the fixtures come thick and fast.

With the rain continuing to pour down chances were becoming thin on the ground but with seven minutes left Hearts passed up a glorious opportunity to kill the tie.

Boyce's effort was deflected into the path of Euan Henderson who had time to pick his spot but rushed his effort from eight yards out, the ball clipping the bar as it sailed over.

The game became more stretched as Falkirk desperately searched for an equaliser, but Hearts held on comfortably in the end and march on to the quarter-finals.

'We played like the weather' - reaction

Falkirk players 'devastated' at cup defeat - David McCracken

Falkirk co-manager David McCracken: "It was tough to take. The pleasing factor for us though was the way we reacted to going behind. It's a fine line that we didn't take the opportunities - I think we actually created more than Hearts."

Hearts manager Daniel Stendel: "Our game was like the weather, not really great, but it was just important we got into the next round, it's very positive for us. Falkirk invested a lot of things in the second half but we let them come back into the game. We controlled the game but made some easy mistakes."

Hearts 'had some luck' against Falkirk - Stendel