The win was the Accies’ first away Scottish Premiership victory since early October and leaves them in third place, while the struggling Staggies remain second from bottom.
The visitors took the lead on six minutes when Canning rose above the home defence to power home a header from Ali Crawford’s corner.
Martin Woods almost pulled Ross County level on 15 minutes with a wonderful free-kick from 25 yards out but Michael McGovern just managed to push the ball onto the post.
Woods had another chance minutes later when Joe Cardle cut the ball across the box but the former Barnsley man fired wildly over.
Mickael Antoine-Curier got a good sight of goal soon after the interval after some good build-up from Hamilton but his low shot from the edge of the box was well saved by Antonio Reguero.
Cardle had a good header saved by McGovern as County applied pressure late on but they were unable to force an equaliser and it ended as another frustrating outing for Jim McIntyre’s side.