Robbie Neilson's men led 2-0 at the break thanks to strikes from Liam Boyce and substitute Euan Henderson, who replaced an injured Josh Ginnelly early on.
Rovers were reduced to 10 men before half-time when Regan Hendry was shown a straight red card for a stamp on Andy Halliday.
The intensity dropped after the break until new signing Armand Gnanduillet came off the bench to bag an impressive late double to add gloss to a final scoreline Hearts fully deserved.
The perfect response to Saturday’s dismal 3-2 home defeat to the Kirkcaldy side. So, how did the players involved 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.
1. Craig Gordon - 6
A brilliant penalty save to deny Hendry. The third goal squeezed through him for Tumilty to score. Photo: Ross MacDonald - SNS Group
2. Michael Smith - 4
One of his poorest games in a Hearts shirt. Often on the back foot due to the threat of Kai Kennedy culminating in the concession of a penalty. Did create an opportunity for Mackay-Steven. Photo: Mark Scates - SNS Group
3. Craig Halkett - 3
The centre-back, and Hearts, afternoon was summed up by Kennedy leading him a merry dance in the build-up for the third goal. A ragged defensive display. Photo: Mark Scates - SNS Group
4. Christophe Berra - 4
Misunderstanding with Kingsley led to the corner where the opening goal was scored from. Replaced before half-time due to injury. Photo: Mark Scates - SNS Group