A rare goal from Bert Konterman gave Rangers the win they needed to regain second place above Hibernian.
Incredibly they had to survive two missed penalties at Dens Park with Dundee striker Juan Sara being the man to waste both spot kicks.
Scott Wilson had brought Sara down for the first but the Argentinian's response was one of the most wayward spot-kicks in Scottish footballing history.
His second, which followed a Lorenzo Amoruso foul on Claudio Caniggia, was closer but still wide of Stefan Klos' goal.
Amazingly, the game also saw a third penalty miss, with Rangers substitute Billy Dodds the guilty man late on.
The first half began in a blizzard and Rangers launched a flurry of attacks that saw Tore Andre Flo twice denied by Dundee goalkeeper Marco Roccati.
The first was a tip round a post after Tugay and Barry Ferguson had combined to locate a big enough hole in the home defence for the Norseman to get a clear sight of goal.
Minutes later he was in again, with Tugay again involved, but Roccati came off his line to block Flo's attempt to loft the ball over him and the ball appeared to bounce off Steven Tweed's arm as he moved in to clear.
Almost 20 minutes were on the clock before the home side mustered a decent attack against a new-look Rangers side that saw Lorenzo Amoruso back from injury and Konterman pushed up into midfield.
It was worth waiting for as new signing Alberto Garrido, who had only arrived the day before, planted the ball on to the head of Claudio Caniggia.
It was a clear chance but his finish was disappointing to say the least.
But he almost made amends straight away by sending Sara through and Stefan Klos in the Rangers goal had to come off his line to make an important block.
A samba band was in the crowd to give musical accompaniment to any excitement produced by the home side but there was little on show until the final minute of the half.
That was when Sara went down under Scott Wilson's challenge right on the edge of the box and immediately the Rangers players, with Amoruso leading the way, began berating the linesman who had signalled to referee Hugh Dallas that it was indeed a foul challenge within the area.
In the end it did not matter as the striker took it himself and produced one of the most inaccurate spot kicks inn living memory, blasting it both high and wide into a startled section of the crowd.
The snow had long since stopped by this point and the second half was played in bright sunshine.
It did not take long before Javier Artero had clipped the Rangers bar with an effort that followed Giorgi Nemsadze's clever lay-back and it was the Georgian who was the game's outstanding performer overall.
Amoruso, of course, had marked his two previous visits to the city, both at Dens and United's Tannadice, with howling errors that cost four valuable points.
The Italian had his moments on this occasion as well, with some alarmingly wayward passing near his own goal but managed to go unpunished until his fateful slide in on Caniggia.
It was a relieved Italian who watched Sara miss from the spot again as the Argentinian slotted wide this time.
Then came Konterman's goal from a free-kick move and the stalled Rangers bandwagon was rolling once more.
Newcomer Alberto Garrida went down in the box after Tugay had given him a nudge but Dallas was not tempted to give Sara an opportunity for a rare hat-trick of misses.
Yet Dallas was to point to the spot once more, at the Dundee end.
Substitute Billy Dodds, who had come on for Allan Johnston early in the second half, went down under Steven Tweed's challenge and elected to take it himself.
But it was not a day for spot kickers and Dodds marked his return from injury with a miss of his own, trundling the ball wide of a post.