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.
9. Josh Ginnelly - 5
Not the best outing for the Englishman. At times he hesitated before going at his opponent. But every road the winger did try to run down seemed to be a dead end with Stirling very well organised. Wide men can have games like this. Photo: Paul Devlin - SNS Group
10. Liam Boyce - 7
Got his goal but all in all a relatively quiet evening for the Northern Irishman. Some nice one-touch play but at times it was too tight for it to come off. Photo: Paul Devlin - SNS Group
11. Gary Mackay-Steven - 7
A simply brilliant piece of magic to set up Liam Boyce with a flick of the boot. However, he really should have got on the scoresheet in the first half but decided to pass up the opportunity. Photo: Paul Devlin - SNS Group
12. Armand Gnanduillet - 6
Good hold up play and went close with an effort which was saved by Currie. Photo: Craig Williamson - SNS Group