Unted were beaten in the Scottish Cup by Motherwell in midweek but secured a surprise victory with David Goodwillie's last-minute strike.
Nikica Jelavic's opener was cancelled out by David Robertson on the stroke of half-time. Steven Naismith restored Rangers' lead shortly after the restart only for United to level for a second time through Johnny Russell.
Not satisfied with the point, the Tannadice side then sealed victory thanks to one-time Rangers target Goodwillie, who this week signed a new deal.
Houston said: "I don't think we could have asked for a better response. I've got a group of players who will respond and who have responded in the past to a couple of dodgy results.
"To twice come from behind against a good Rangers side shows their resilience and determination so I can't praise them highly enough."
Source: PA
Source: PA