County had made the better chances throughout but the Bully Wee soaked up the pressure and grabbed the winner with 20 minutes remaining.
Clyde won a free-kick just outside the box in the fifth minute, but Aaron Conway's delivery was headed clear by Stuart Malcolm.
At the other end, Mark McCulloch sent over a sweeping cross but there were no takers in front of goal.
County should have taken the lead in the 18th minute when John Rankin got on the end of a Don Cowie cross which was parried by keeper Bryn Halliwell then Alex Burke saw his shot fly over the crossbar.
Play was pretty easy at this stage with the visitors prepared to send players forward in numbers and Conway sent in a long-range free-kick that was easily held by Colin Stewart.
County were creating the better chances and Cowie tested Halliwell with a fierce low drive.
Then Gary McSwegan had a shot deflected past for a corner as the home side pressed hard for the opener.
A slip by Stewart almost cost Country dear, but the keeper recovered his footing in time, before Harty could take advantage.
County were really pushing and a Rankin cross was spilled by Halliwell and new signing Fergus Tiernan's goalbound effort was tipped over the bar by the Clyde keeper.
The visitors produced the first opening of the second half, when Harty played a neat one-two with Alex Walker and rolled the ball just past the upright.
Clyde's Jimmy Gibson and County's Jim Lauchlan joined Malcolm in the referee's book although there was little in the way of dirty tackles.
The game burst into life on the hour mark when David Winters was beaten to a high ball which fell for Burke whose shot was pushed away by Halliwell.
But it was Clyde who took the lead in the 70th minute when Harty slotted away Gibson's layoff.
Burke had another chance to get on target shortly afterwards but he miscued his hot right in front of goal.
That was County's last real chance of the game as Clyde held out for the win.