Robbie Neilson’s men ran out 2-0 winners at Forthbank Stadium thanks to goals from Liam Boyce and Finlay Pollock.
It means that the Tynecastle men have a game to spare when they welcome Inverness CT to Gorgie on Sunday before the start of the cinch Premiership with three wins from three in the League Cup.
Hearts were given something to think about by their League Two opponents who threatened with pace up front and were very well organised but the quality shone through in the end.
How did the visiting players rate out of ten?
Player ratings scale - 10: One of the best performances you've seen. 9: Outstanding. 8: Very good. 7: Good. 6: Average. 5: Poor, 4: Very poor. 3: A terrible day at the office. 2: Abysmal. 1: One of the worst performances you've seen.
5. Michael Smith - 6
Not as influential going forward as he was against Cove Rangers. Some nice recovery work in the first half and covered well in general. Photo: Craig Williamson - SNS Group
6. Andy Halliday - 6
Put Hearts in trouble early on with a slack pass. Was given more freedom to push forward and support the attack but struggled to get the ball in space against a compact opponent. Made a brilliant forward run in the second half which was crudely stopped at the edge of the box. Photo: Paul Devlin - SNS Group
7. Peter Haring - 6
Lovely slide tackle to stop Stirling and set up a counter in the first half. Sat at the base of the midfield and protected, but wasn't a hugely influential in directing the game. Photo: Paul Devlin - SNS Group
8. Alex Cochrane - 7
Got forward early in the first half to stretch the game but at times dropped too deep. Switched with Kingsley naturally. Set up the second goal with a nice centre. Photo: Paul Devlin - SNS Group