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.
5. Stephen Kingsley - 3
Easily his poorest display since joining the club. Misunderstanding with Berra before the first goal and conceded a penalty which was missed. A messy outing rather than a calm and controlled one fans are used to. Photo: Mark Scates - SNS Group
6. Andy Irving - 6
Had a lot to do and cover in midfield. One of the few players who wasn’t really poor. Made a brilliant pass for Ginnelly to set up Naismith for a chance. Photo: Paul Devlin - SNS Group
7. Andy Halliday - 3
Struggled to impose himself on the game in anyway. Played too deep at the start going by encouragements from Neilson and Naismith. Hooked for Walker in the second half. Photo: Mark Scates - SNS Group
8. Gary Mackay-Steven - 4
Didn’t get a chance to showcase his qualities in the first-half. Some positive runs in the second but couldn’t unlock the Raith defence. Photo: Paul Devlin - SNS Group