Unconvincing Rangers ended Dundee United's eight-game unbeaten run to leapfrog their hosts into third place in the Scottish Premiership and move back to within five points of leading duo Celtic and Aberdeen.
Tom Lawrence's early goal was enough for the visitors to navigate what was viewed by many as a must-win game for their title hopes, even this early in the season, after their 3-0 Old Firm derby loss last time out.
The Wales midfielder pounced on Cyriel Dessers' flick and showed some nice footwork before cutely chipping over advancing goalkeeper Jack Walton after only seven minutes.
It was the first time United had found themselves behind since their return to the top flight and, as they struggled to respond, manager Jim Goodwin replaced Kevin Holt with Ross Docherty in central midfield before the break.
After a change of shape, with Vicko Sevelj on for yellow carded Emmanuel Adegboyega at half-time, United crept more into the game.
Ever-impressive winger Kristijan Trapanovski sent a couple of drives wide as Rangers were forced ever deeper into their own half.
Dessers had been denied by Walton at the front post shortly before the break, while Lawrence curled a drive just over the crossbar and was thwarted by a big hand from the goalkeeper.
Otherwise, though, Rangers were rarely in full control and were happy just to see the game out to collect a much-needed three points.
Having lost all 11 of his previous meetings with Rangers as a manager, it was perhaps no surprise Goodwin had the modest aim of finishing the day still ahead of Rangers given he viewed this as his side's "toughest test" so far.
On the back of three consecutive wins, Goodwin named the same XI for a fourth game in a row as United sought to extend their unbeaten home run to 11 games - six of those coming this season.
He was "not getting carried away" with that start, though, and his caution seemed justified as Rangers dominated early proceedings.
However, bringing on Docherty before the break and Sevelj at half-time changed the flow of the game as a disjointed Rangers struggled to attack up the notorious Tannadice slope.
United, though, were unable to force Jack Butland into a serious save and will surely see this as an opportunity missed to take advantage of the first time they have gone into a game ahead of Rangers in the league since 1993.
The mood around Rangers was not helped before kick-off with Saturday's news that chairman John Bennett, who has invested heavily in the club in recent years, had stood down for health reasons.
The Ibrox club were already seeking a new chief executive and a new academy director, while they have just returned to Ibrox after having to spend money hiring Hampden because of delayed renovation work.
Despite it all, manager Philippe Clement insisted in last week's question and answer session with supporters that he believes his side can still win the title and this was always going to be a severe test of those credentials.
Illness denied him of the services of Czech Republic international Vaclav Cerny and, with Rabbi Matondo injured, Kieran Dowell was forced into an unfamiliar wide role.
Rangers could not have asked for a better start as their early intensity forced a goal.
It is kind of game you would expect City rivals Celtic to dominate thereafter, but this Rangers side failed to build on that and never looked like one a class above their less expensively-assembled hosts.
Dundee United manager Jim Goodwin: "We’re frustrated the unbeaten run has come to an end. I don’t have too many arguments about the end result – Rangers created two or three goalscoring opportunities, whereas we didn’t create anything.
"In the second half, we were a lot better and penned Rangers back for large periods, but for all the possession we had, we just didn’t create anything of real worth."
Rangers manager Philippe Clement: "It's a big result because it's a hard place to come to. The players did a really good job.
"It's massive to start the game really well. The only thing we missed was scoring the second goal to kill off the game - then you're more comfortable. We didn't give away chances - that's another good thing."