Andy Halliday opened the scoring with a near 30-year daisy cutter before Liam Boyce added a second before half-time. Gary Mackay-Steven completed the scoring with a fizzing shot from the edge of the box after the interval.
Cove Rangers had their moments at the start of the match before Hearts got to grips with the game.
There were 2,000 fans in attendance to witness their first Hearts game at Tynecastle since March 2020 and they would have been happy with what they saw.
A number of players impressed for the home side. How did the 16 involve 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.
. EDINBURGH, SCOTLAND - JULY 13: Hearts' Andy Halliday (centre) celebrates making it 1-0 during a Premier Sports Cup tie between Heart of Midlothian and Cove Rangers at Tynecastle Park, on July 13, 2021, in Edinburgh, Scotland. (Photo by Ross MacDonald / SNS Group)
How the players rated against Cove Rangers. (Photo by Ross MacDonald / SNS Group) Photo: Ross MacDonald - SNS Group
. Craig Gordon - 7
Important save early on to take the pace off a Leighton McIntosh shot. Rarely tested after that and makes club history with his ninth consecutive clean sheet. Photo: Paul Devlin - SNS Group
. John Souttar - 7
A comfortable evening for the centre-back. Assured in possession, his usual positivity with the ball, strong in the air. Photo: Paul Devlin - SNS Group
. Craig Halkett - 6
Couple of moments in the first half where he was caught off guard by a Cove forward and playing catch-up. But settled and was solid for the remainder of the game. Photo: Paul Devlin - SNS Group
. Stephen Kingsley - 6
Untroubled throughout but a useful 57 or so minutes as he builds back to full fitness. Protection in front with Alex Cochrane makes the left side a solid area of the pitch for Hearts. Photo: Paul Devlin - SNS Group
1. Craig Gordon - 7
Important save early on to take the pace off a Leighton McIntosh shot. Rarely tested after that and makes club history with his ninth consecutive clean sheet. Photo: Paul Devlin - SNS Group
2. John Souttar - 7
A comfortable evening for the centre-back. Assured in possession, his usual positivity with the ball, strong in the air. Photo: Paul Devlin - SNS Group
3. Craig Halkett - 6
Couple of moments in the first half where he was caught off guard by a Cove forward and playing catch-up. But settled and was solid for the remainder of the game. Photo: Paul Devlin - SNS Group
4. Stephen Kingsley - 6
Untroubled throughout but a useful 57 or so minutes as he builds back to full fitness. Protection in front with Alex Cochrane makes the left side a solid area of the pitch for Hearts. Photo: Paul Devlin - SNS Group