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.