It was Gers’ first loss in 25 domestic outings and their first loss in the competition since they were beaten by Dunfermline at East End Park in January 2007.
Now Walter Smith’s men only have the SPL to focus on, although their hopes of retaining that have been boosted by Celtic’s surprise 4-0 thumping at St Mirren tonight.
That means they remain 10 points clear of the Parkhead team in the title race with two games in hand.
That is at least some consolation for the league champions – although there is huge disappointment at the possibility of a Scottish clean sweep disappearing.
Smith made seven changes to the team that beat St Mirren to the League Cup at Hampden as he went into the game with one eye on Saturday’s SPL clash with Hearts.
Allan McGregor took back his usual position in goal, replacing Neil Alexander, and the current first-choice defence remained in place.
Elsewhere, there was an unfamiliar look to the midfield as the ill Steven Davis missed out and Gers’ appeal against Kevin Thomson’s weekend red card was dismissed.
In their absence, Steven Naismith and Mo Edu teamed up in the centre and had DaMarcus Beasley and Kyle Lafferty either side of them.
In attack, it was down to youngsters Andrew Little and John Fleck to test home keeper Dusan Pernis as Kris Boyd and Kenny Miller dropped to the bench.
United were first to attack and Jon Daly’s fierce shot from the edge of the area brought out an excellent save from McGregor.
Morgaro Gomis’ shot was blocked after the resulting corner came in then Mihael Kovacevic’s effort dipped just past the far post as the hosts laid siege to the away goal.
At the other end, Fleck went on a mazy run and deserved better than to see his pulled shot rebound off an opposition defender and away.
Rangers took a bit of time to settle into the game and with such a disjointed look to their team, that wasn’t too surprising.
By and large, the Arabs made a regular habit of coming forward and Smith’s team simply punted the ball upfield all too often as they looked short of ideas.
It took two superb tackles from Steven Whittaker to stop Peter Houston’s men in dangerous positions as the Light Blues spent much of the first half on the back foot.
A fantastic run by home striker David Goodwillie took him past three defenders in a tight corner and Naismith almost turned his low cross into his own net but the ball crept wide.
United had a good claim for a penalty turned down when the ball seemed to strike Lafferty’s arm when he was under pressure from Daly after Craig Conway’s free kick.
So fierce were the Taysiders’ protests when the kick wasn’t given that defender Garry Kenneth was booked for his furious tirade at linesman Martin Cryans.
Temperatures were rising and at last Gers were adapting, though they were still struggling to get anywhere near Pernis’ upright.
Much like they did at the National Stadium against Saints three days earlier, they were being restricted to defending in numbers at times then attacking on the counter.
One such foray upfield nearly paid off for them when Lafferty fed Naismith and he broke forward before teeing up Fleck, who hit the side netting before seeing an offside flag.
When Darren Dods was clumsy in possession moments later and Fleck broke forward again, he should have set up Edu but found himself running into trouble instead.
Rangers actually finished the first half playing their best football yet and for that reason, they emerged after the break unchanged.
The game had developed into a more even contest and that continued to be the case once play got going again, with each side taking turns to come forward.
Sasa Papac almost drifted a deep free kick from fully 45 yards in at the back post after a foul on Beasley by Robertson.
At the other end, Conway’s shot was almost flicked in unintentionally by Daly but a wonderful scrambling stop by McGregor kept it out.
With an hour gone, the match was really hanging in the balance and Lafferty had a great chance to swing Rangers an advantage.
But after a good threaded pass by Beasley, Dods’ fine tackle stopped the Ulsterman in his tracks as he prepared to pull the trigger.
Lafferty was having a good game and looked far more confident than he has done in recent weeks.
He had one blistering run which took him away from a clutch of United defenders and had he got past one more, he would have had a shooting chance inside the box.
For the first time in the match, the away side was on top and Smith looked to capitalise by throwing on Nacho Novo for the ineffective Fleck.
The Spaniard’s first contribution was to set up Lafferty and his dipping half volley wasn’t far from dropping under the crossbar.
Little had had a quiet game but had an excellent chance to find the net as the regulation 90 minutes moved its last quarter hour.
Beasley found him with a cross from the left corner but when it fell to the youngster eight yards out, he just didn’t connect with it properly and Pernis saved gratefully.
Lafferty’s night came to a premature end when he went off with cramp and that allowed for an appearance by cup final matchwinner Miller.
His first chance came when he played a neat one-two with Novo but although he struck his 15-yard shot well enough, Pernis was in the right place to stop it.
Beasley then swung a hard cross back into the six-yard box which took a crucial touch off a flying United defender and took it away from the waiting Miller.
With full-time approaching, Rangers looked the more likely side to win it and were enjoying better possession.
But when Goodwillie netted less than four minutes from full-time only to be flagged off, there was a big warning to the Ibrox side that they could just as easily lose.
McGregor was at his outstanding best moments later when he dived at full stretch to deny Daly.
But just when it seemed the game was heading for extra-time, United snatched victory with a minute of the game remaining.
A hopeful ball was flung into the box and when McGregor attempted to block it, the ball cannoned off Robertson and into the back of the net.
The home support erupted and away fans, previously buoyant at news of Celtic’s capitulation in Paisley, were suddenly quiet.
The treble dream was dead and now Rangers’ focus is on finishing the season with a second successive SPL title.