Sloppy defending contributed to United’s third goal 11 minutes from time and then it got rather embarrassing as firstly Kal Naismith and then Ian Black were sent off.
In truth it indicated the difference in strength between the two sides but it could have been and should have been a more even contest and that will be the big disappointment.
It was probably just as well there were hardly any Rangers fans in the ground to see it.
The start could have hardly have been more disastrous as Rangers went behind virtually straight from the kick-off.
There were only 15 seconds on the clock when Johnny Russell’s left foot shot squirmed into the net despite the best efforts of Neil Alexander.
It was as a result of desperately poor defending as firstly Lee Wallace was beaten in the air by Jon Daly to a diagonal ball and then Emilson Cribari and Ross Perry got in each other’s way allowing the ball to reach Russell.
Calamitous barely describes it all and Ally McCoist could scarcely believe his eyes.
Rangers nearly found an equaliser within a minute when Andy Little found space in the box after good work from David Templeton but Little pulled a left foot shot just wide of the right post.
However, it was a rare moment of offensive play in the early stages as the Light Blues were fortunate not to concede on two more occasions before 17 minutes had been played.
The centre of the Rangers defence again looked weak in six minutes when Russell headed inches wide from a Barry Douglas cross.
Then the Dundee United front man hit the crossbar with a left foot shot in 16 minutes after another Daly flick on and Rangers were struggling to hold on.
During this period Lee Wallace was booked for a foul on Gavin Gunning but it was his play down the left side that began to give Rangers a foothold in the match.
He and Templeton began to link better and finally put some pressure on United. Indeed in 27 minutes the acting captain produced a terrific cross which Fran Sandaza should have done better with instead of glancing a header wide.
However, terrible defending was Rangers’ downfall again in 36 minutes when United scored a second goal.
No-one picked up Daly as a long free kick from the left back area came into the penalty area and he guided a header past Alexander. He was so alone that he seemed to be offside but replays showed that he was not.
An already tough task suddenly became incredibly difficult and it was exacerbated by enforced changes.
Perry suddenly slumped to the turf and indicated to the bench that his game was over and Chris Hegarty came on as a straight replacement.
That happened five minutes before half-time and during the break it became clear that Sandaza’s hamstring problem would force his withdrawal and Kal Naismith was thrust into the action.
There were also yellow cards for Kyle Hutton and Cribari in the period just before the break for fouls on Gary Mackay-Steven and Willo Flood respectively.
Perhaps a combination of Rangers’ determination and United’s contentedness with the score resulted in much better possession and pressure in the early part of the second half.
Wallace was at the heart of most of the good play but Rangers could not seem to carve out an opening,
The closest they came in this spell was a long-range, swerving shot from Ian Black in 62 minutes which was only just past the right hand post.
Templeton was more involved and had a long range shot comfortably saved by Cherzniak and then came close to picking out Little in the box with a good cross.
However, the frustration for the bench was the lack of a killer pass or a meaningful test of the United keeper.
Rangers’ inability to really worry United meant that the tie slowly slipped away and the loss of a third goal 11 minutes from time only rubbed salt into the wounds.
Again indecisive defending was a contributory factor and when Faure looped a header into the air United were quicker to react with Daly threading a ball through to Russell who got in behind Wallace to steer the ball past Alexander.
Sadly Rangers lost their discipline in the final moments when both Naismith and Black were sent off.
Youngster Naismith showed his inexperience in 85 minutes when he made a wild challenge on Flood right in front of the referee and was shown a red card.
Then a minute later Black, who had been unfortunate to be booked in 76 minutes for a clash with Gunning, went in rashly on John Rankin and was shown a second yellow and therefore a red.
A disappointing day turned into a rather embarrassing one.
DUNDEE UNITED: Cherzniak; Watson, Gunning, Dillon, Douglas, Flood, Rankin, Armstrong (Ryan 67), Mackay-Steven (Gardyne, 67); Russell, Daly.
Subs not used: Banks, Millar, McLean
Booked: Gunning (76)
RANGERS: Alexander; Faure, Perry (Hegarty 40), Cribari, Wallace; Black, Hutton; Little, Shiels (McKay 72), Templeton; Sandaza (Naismith 45)
Subs not used: Gallacher, Crawford.
Sent off: Naismith (85), Black (86)
Bookings: Wallace (5), Hutton (40), Cribari (45), Shiels (70)