The Terrors fell a goal behind when Iain Vigurs headed home in the 49th minute but managed to fight back thanks to goals from Johnny Russell and Stuart Armstrong to record their first win in three league outings.
Houston heaped praise on his side, who now sit seventh on the Scottish Premier League table, saying they showed plenty of fight to get back into and eventually win the contest.
"Again we went a goal behind but we showed great character and got a goal back fairly early after Ross County scored," he said.
"From there on in I only thought there was going to be one winner. We created a few chances and I'm delighted with the three points.
"It was a tough, tough match. To come up here and get a win was never going to be easy. Other teams have struggled up here, so I have to give my players great credit for getting the three points.
"I've got to mention, I thought our supporters were magnificent. They cheered the team from the start right to the final whistle."