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.
9. Steven Naismith - 5
Barely seen the ball in the first half. Foraged in the second half without taking control of the game or producing a bit of magic. Went close with a header which hit the bar. Photo: Paul Devlin - SNS Group
10. Elliott Frear - 3
After his goalscoring exploits last week, the winger was largely anonymous. His replacement was on the pitch a matter of minutes before providing something of substance. Photo: Mark Scates - SNS Group
11. Liam Boyce - 6
Anonymous in the first-half and faced the ire of Neilson. Scored twice in the second and was much more involved in the build-up. Photo: Ross Parker - SNS Group
12. Jamie Walker - 5
Should have scored when presented with a great opportunity 10 yards out but shot tamely at MacDonald. Photo: Mark Scates - SNS Group