Olly Lee opened the scoring after just 20 seconds with a back post finish and doubled his own and his team’s tally a minute later with a shot from an Elliot Frear corner.
East Fife hit back through Jack Hamilton to reduce the deficit before half-time although Andy Irvine restored Hearts’ two-goal advantage with a long-range stunner midway through the second half.
The home side hit back immediately though through Ryan Wallace and the Robbie Nielson’s men had to hang on for victory in the closing stages. Here's how the Hearts players rated on the night:
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.
1. GK - Ross Stewart - 7
Made a reflex save to preserve Hearts' lead at 2-1 and was entitled to expect his defence to help him at the first after getting a strong hand to the initial effort. Photo: Mark Scates - SNS Group
2. RB - Jamie Brandon - 6
Didn't have the best of nights, lost his man a few times and part of a defence that was unconvincing all night. Photo: Rob Casey - SNS Group
3. LB - Aidy White - 6
Another member of the back four who failed to convince. Got forward well at times but didn't defend particularly well, especially in the final minute when he allowed Watt to get in behind and almost equalise Photo: Ross Parker - SNS Group
4. CB - Mihai Popescu - 5
Caught wrong side of his man for East Fife's second and never quite got to grips with the movement of Wallace. Photo: Ross Parker - SNS Group