The champions are in top form and preparing to welcome Italian giants Juventus to Glasgow in the Champions League for their forthcoming clash.
But Houston, who side beat Kilmarnock in last weekend's five-goal thriller at Rugby Park, knows his team have to have the necessary self-belief that they can go to the home of the champions and halt them in their tracks.
Houston said: "It's always the same when you go to Parkhead. Not many people will be giving us a chance outwith ourselves so that's where we have to have the necessary belief.
"There's no point thinking otherwise. We have to go there and think positively and really feel we can do something. If we focus along those lines then anything is possible."
United came from behind to earn a last-gasp 2-2 draw with the Hoops on Tayside back in November when Efe Ambrose headed in a late own goal.
And Houston hopes they can take confidence from their last outing.
He said: "We showed we can do it that day. We didn't start the game all that well but stuck to it and got our rewards in the end.
"We should be relishing this opportunity to go and play at one of the best venues around and hopeully my players respond to the challenge on the night."
United welcome back midfield pair Stuart Armstrong and Richie Ryan from injury while defender Brian McLean is free from suspension.