Houston made four changes ahead of a hectic schedule with Danny Swanson, Mogaro Gomis, Barry Douglas and Stuart Armstrong coming in. But his team pushed into the top six with several games in hand on their rivals.
"I'm pleased with the players because this was a very difficult game," Houston said.
United needed goals from substitutes Prince Buaben and David Robertson in the final 16 minutes to claim the points but Houston was delighted with his squad.
Houston added: "We knew it was going to be a difficult game and I felt that Inverness felt they had to win because they were talking about how they had Motherwell on Saturday as well and they maybe fancied their chances.
"But I freshened it up a wee bit because we have a lot of games coming up and I felt the boys that came in did well.
"I thought we played the better football. We passed the ball well and we don't have a lot of height in the team so we have to pass it and we played round them at times.
"It's always a concern where a goal is going to come from and I felt young Stuart Armstrong was starting to tire a wee bit, but it's good that we have got a player like Prince Buaben - who was just rested - goes on the park and within a couple of minutes scores a goal.
"David Robertson just happened to score as well but I was also pleased with Andis Shala's contribution because he had one kicked off the line and one screwed just by the post.
"So when you come up here, create chances, score a couple of goals and go away with a clean sheet you have got to be delighted and I am."
Source: PA
Source: PA