Gary Mackay-Steven used his pace to open the scoring in the first half with Liam Boyce doubling the lead after the break thanks to some good build-up play involving Peter Haring and Michael Smith.
Hearts could have won the game more comfortably but passed up a few opportunities in each half.
Robbie Neilson will likely be pleased with his team, considering it was their first competitive action in more than 70 days and the fact Hearts lost on their last trip to Balmoor.
How did the players 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.
Robbie Neilson will likely be pleased with his team, considering it was their first competitive action in more than 70 days and the fact Hearts lost on their last trip to Balmoor.