Rangers added a new chapter of woe to the horror story that season 2000-01 has become for the fallen icons of Scottish football.
A gem of a goal from Claudio Caniggia and a stoppage time clincher from substitute Steven Milne gave Dundee deserved victory just days after neighbours United had knocked Rangers out of the Scottish Cup.
This match, just as on Sunday, was also marked by a Rangers player sent off for two brainless challenges.
At Tannadice it was Bert Konterman and tonight it was Craig Moore who paid for his rashness with two yellow cards.
Rangers have found nothing but misery playing teams from the City of Discovery this season, with the only startling revelation being their rampant indiscipline.
With so many big names on the treatment table it is astonishing how many fit players have joined them on the sidelines through suspension this season.
The result does not change Rangers' position but represents a wasted chance of extending the gap over Hibernian, who had lost at Aberdeen last night.
As for Dundee, it further underlined the conclusion that they should be far higher up the table than they actually are.
Rangers had begun with bluster if not a great deal of confidence and dominated the opening minutes without creating anything too dangerous.
Dundee's first attempt at a reply was sublime and Caniggia was the man who turned a clever move into a memorable goal.
It began with Giorgi Nemsadze's free-kick which was easily repelled by Craig Moore but also straight back to the Georgian.
He switched play to the right flank where Barry Smith combined with Javier Artero to gain ground and slip the ball to the Argentinian in the box, who had somehow lost his marker on the way.
He still had plenty to do as the angle was tight, but his answer to a difficult geometry problem was to smack the ball past Stefan Klos via his near post.
Rangers' reply was immediate and almost led to an equaliser.
Dick Advocaat had handed two players their full debuts - new £900,000 signing Marcus Gayle and young left winger Steven Carson, who had waited four years for the opportunity.
Gayle sent the Ulsterman clear and it needed a sturdy block from Marco Roccati in the Dundee goal to deny him.
It looked as though the home side had been stung into furious reaction but in the end the better chances before the break fell to the away side.
Juan Sara, the man who had missed two penalties in the Dens Park clash a little over a fortnight before, perhaps should have done better when a Scott Wilson error presented him with a sight of goal. His shot was on target this time but Klos was able to save.
Gavin Rae, who scored the winner at Ibrox last season, was guilty of wasting an even better chance after Artero and Caniggia had combined on a right flank that was once again being patrolled by Sergio Porrini, the right-footed left-back whose Ibrox days are fast running out.
Caniggia crossed and Rae timed his run to perfection before screwing the chance wide.
Once again a makeshift midfield line-up featuring the hapless Konterman failed to create anything for Gayle and Tore Andre Flo to feed on during the break.
Moore, the right-back, gave Flo a long ball to chase but the Norseman wasted the opportunity by crossing into Roccati's hands.
Carson had not been afraid to have a go and had won more applause for his efforts than many a team-mate but hie full debut was over at half-time, when Billy Dodds replaced him.
But within seconds Moore's double dose of stupidity had ensured his side were a man down and trailing for the second successive game.
First Moore went into the back of Sara, injuring the back of the striker's head. Literally seconds later he conspicuously scythed down the same man on the touchline.
Caniggia ignited an already volatile atmosphere with a blatant dive on the edge of the Rangers box, for which he was booked.
But there was nothing suspicious about his next contribution and it needed Klos to deny him a second when Rae had put him clear.
Rangers made a tactical reshuffle, with defender Robert Malcolm, who had celebrated his first Scotland Under-21 call-up earlier in the day, replacing Allan Johnston to fill the gap left by Moore. Barry Ferguson was soon booked for a foul on Beto Garrido.
Flo then blazed a good chance over before Artero was booked for fouling Konterman.
When Dodds got the ball at his feet in the box he tumbled over under a challenge but play went on.
Nemsadze was denied an injury time clincher by a timely deflection and from the corner Caniggia headed just over.
But then substitute Walter Del Rio sent a superb ball to the far post where fellow replacement Milne, who had come on for Sara, headed the second goal.
Thousands of home fans had already left by this time anyway.