The Tannadice team dug deep to deliver a late 2-0 win over third-placed Hearts on Wednesday night thanks to Johnny Russell's double.
After a series of winter postponements, United were playing their fourth game in 10 days but showed a never-say-die spirit to rack up a fourth straight Clydesdale Bank Premier League victory.
Despite missing the likes of Garry Kenneth, Prince Buaben, Craig Conway and Scott Severin, Houston's men leapfrogged Kilmarnock into fourth place and moved to within 12 points of Hearts, with a game in hand.
Houston said: "I can't praise the boys highly enough for their second-half performance. Instead of them getting tired, they just got stronger. As a team, I think we played really, really well and we worked very hard.
"It's incredible, we'll recover on Thursday and get ready to pick a team for Inverness (at home on Saturday). It's a small squad but it's close-knit, you can see how they work for each other. I think we deserved our victory, it was a tight game and I always thought the first goal could win it."
Source: PA
Source: PA