Houston knows Ally McCoist's men will still be hurting from Sunday's 3-0 defeat by Old Firm rivals Celtic which brought to an end their recent on-field resurgence amid their on-going financial woes.
The Tannadice side head to Glasgow still chasing their Champions League dream – they are five points behind third-placed Motherwell with three games left this season.
United, who are gearing up for an Old Firm double- header – Celtic head to Tannadice on Sunday – won 2-0 on their last visit to Ibrox, in the Scottish Cup in February and Houston insists for them to make it back-to-back wins at Ibrox, his side will have to get the better of a team who will be keen to make amends to their supporters for Sunday's Parkhead loss.
He said: "Rangers are always dangerous when they're wounded. They'll want to get back in the good books of their own fans again so we'll have to be at our best if we're to win.
"You have to remember Celtic played exceptionally well on Sunday. Up until then, Rangers' form had been really good. We beat them at Tannadice in the league back in March and I thought we were fortunate to beat them, which I actually said after the game.
"But they've strung some good results together since then and we know that when they've taken a defeat from their nearest rivals they will be disappointed.
"They'll be thinking that the best way to get that defeat out of their system is by having a game so quickly, which they will be happy about and we'll have to be on our guard for that."
United are relishing the trip to face Rangers where they will be bidding to keep the pressure on Stuart McCall's side in the hope of forcing a winner-takes-all final-day showdown at Fir Park but should they end up missing out on that coveted third spot which would seal entry to the Champions League qualifiers due to Rangers difficulties, Houston is adamant his players have every right to be proud of their performances this season.
He added: "The players were disappointed by drawing at the weekend but Hearts are a very good side and people forget what we've done this season on a reduced budget.
"The players should be proud of themselves. They've not really achieved anything so far but what they've done is put in a fantastic performance.
"No matter what happens between now and the end of the season, they can hold their heads up high.
"Having said that, we still want to finish as high up the league as we possibly can.There's only three games left so if we can get a victory somewhere I think it could get us at least fourth place. However, that's not to say we're not being ambitious enough to try and get third."