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 ...
9. Alan Forrest
Gave his side impetus after the break, finding his groove and driving things forward. Gave County something to fear. Clinical finish to open the scoring. 7 Photo: Mark Scates - SNS Group
10. Barrie McKay
Another player who exhibited a bit of rustiness and was well shy of his best but showed skills and composure to get what proved to be the winning goal. 6 Photo: Mark Scates - SNS Group
11. Lawrence Shankland
Demonstrated a willingness to graft for the team and tried to work the Ross County defence. Showed potential to link up well with Forrest and McKay. 7 Photo: Ross Parker - SNS Group
12. Substitutes
Jorge Grant (6, above) gave the midfield better balance, Liam Boyce (6) showed nous in working defence, Cammy Devlin (6) provided dynamism and Andy Halliday (6) helped see the game out. Photo: Mark Scates - SNS Group