The Staggies were the better team in the first half and struck the woodwork twice before the break.
But the hosts, relieved still to be on level terms, stepped things up after the interval and got themselves two goals in front before Jordan White hit back to set up a tense finale.
“In the first half, we showed the rustiness of coming into competitive games from pre-season,” said Hearts boss Robbie Neilson, whose team begin their European campaign next month.
“One of the plus sides of being in Europe is you can build into pre-season. But one of the down sides is you’re not involved in the Premier Sports Cup, which I think is a great cup because you can come in and play four games and it’s competitive.
“And I just felt the first half we didn’t have that competitive edge we needed, that energy to break forward.
“The second half was miles better after we spoke to them.”
Moira Gordon was at Tynecastle and rated the Hearts players out of ten ...
5. Nathaniel Atkinson
Completely off the pace, with illness apparently sapping him of energy. Made a last-ditch tackle to deny a County opener but Neilson did him a favour by taking him off after just 28 minutes. 4 Photo: Mark Scates - SNS Group
6. Michael Smith
One of the better starters, he showed drive in the middle of the park and gave his usual steady performance and helped Sibbick when moved to right wing-back. 6 Photo: Mark Scates - SNS Group
7. Peter Haring
Caught on the back foot too often in the first half and lacked the intensity of his opponents. Shook off some of the rustiness but distribution was poor by his standards. 5 Photo: Ross Parker - SNS Group
8. Alex Cochrane
While the whole side struggled defensively in the opening 45 minutes he wasn’t the worst offender and was a bright spark going forward, assisting in both goals. 7 Photo: Ross Parker - SNS Group