Johnny Russell knocked in the equaliser, setting up Stuart Armstrong to nod in the winner just after the hour having trailed to Iain Vigurs' glancing header.
It was the second time in two weeks the Tangerines had to come from behind. They were 2-0 and 3-1 down at home to Kilmarnock before recovering to draw 3-3 eight days ago.
Houston said: "Again we went a goal behind but we showed great character and got a goal back fairly early after Ross County scored.
"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."