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.
. KIRKCALDY, SCOTLAND - JANUARY 26: Hearts players celebrate Euan Hendersons goal to make it 2-0 Hearts during the Scottish Championship match between Raith Rovers and Heart of Midlothian at Stark's Park on January 26, 2021, in Kirkcaldy, Scotland. (Photo by Ross Parker / SNS Group)
Hearts players celebrate as Euan Henderson's goal makes it 2-0 against Raith Rovers at Stark's Park. (Photo by Ross Parker / SNS Group) Photo: Ross Parker - SNS Group
. Craig Gordon - 6
A virtual spectator. No saves, and barely any kick outs to take as Hearts played the game in the Raith half. He won't have had many easier 90 minutes in his long and distinguished career. Photo: Ross MacDonald - SNS Group
. Michael Smith - 8
Much more like himself after Saturday's poor showing. Involved in the slick one-two that led to the all-important opener and contained the threat of Kai Kennedy much better. Photo: Mark Scates - SNS Group
. Craig Halkett - 7
A much more straightforward game for the centre-half than he endured on Saturday. Hardly had to break sweat in the first half but made a couple of good interceptions after the break. Photo: Mark Scates - SNS Group
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