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.
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.
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