Shota Arveladze, Claudio Reyna and Claudio Caniggia – visiting his old ground for the first time – tried hard but Dundee, who had played well in the first half, held firm.
It now means that Thursday’s UEFA Cup return with Paris Saint-Germain has added importance if it was not crucial enough. Should Rangers go out it really would make the season a total misery.
Dens Park has traditionally been a difficult venue for Rangers and despite a decent start they found themselves fortunate to reach half-time still level with Ivano Bonetti’s side.
The Ibrox men won three corners in the first four minutes and Dundee scarcely got a touch but it certainly did not set the tone for the contest as Dundee looked increasingly menacing from about the midway point of the half.
They might have had two penalties if referee Dougie McDonald had been ultra-officious and Rangers can feel fortunate that at least one of the awards was not given.
Michael Ball seemed to trip Juan Sara in the left corner of the Rangers box as he knocked the ball out for a corner but he escaped. Then Craig Moore seemed to bundle Sara to the ground in 25 minutes after Cabellero had crossed from the right but, again, no spotkick was given.
TV evidence, however, indicated that Moore was completely innocent. Indeed, Sara might well have deserved a caution for diving.
Klos had to be at his best to prevent Rangers from going behind in 28 minutes when he pushed Caballero’s shot onto his right hand post after Ketsbaia had played the ball through.
The referee, though, did not give Klos any credit as he awarded a goalkick. The Rangers keeper probably did not mind though.
This was a worrying spell for Rangers, who had failed to test Jamie Langfield at all in the first half. Tore Andre Flo connected with a couple of Claudio Reyna corners but they both flew wide while Shota Arveladze had a shot deflected wide.
That said, Rangers should have taken the lead 10 minutes before the break in a move started by Moore, back in the side after his unsuccessful efforts with the Australian national team.
Moore slid a great pass through for Flo on the right side of the Dundee box. The Norwegian star had the time and space to take it on himself but he tried to play in Arveladze who was in a more central position.
Unfortunately for Rangers, his pass was inaccurate and went behind Shota and the chance was lost. It summed up the first half for Rangers who struggled to cope with Dundee at times, which was clearly a cause for concern for Dick Advocaat.
Presumably there was a frank exchange of views at half-time but whatever happened Rangers were much more purposeful in the early moments of the second half and took a grip of the game.
Reyna was almost in three minutes after the break when Langfield dropped the ball under pressure from Caniggia, but Dundee skipper Barry Smith saved his keeper with a crucial tackle.
Then in 54 minutes the USA captain found himself with an even better opportunity after some great work from Caniggia, who had an increasing influence as the game progressed.
The former Dundee man skipped away from Smith on the right and whipped over a great cross which Langfield could only push into the path of Reyna but the Rangers midfielder shot over the bar with his left foot from 14 yards.
It was a bad miss but it was a further indication of Rangers’ greater threat and four minutes later the Ibrox men squandered another good opportunity.
Flo did the hard work by winning the ball in midfield and then bursting away from Fan Zhiyi to release Caniggia on the right. He raced into the box to take the return from Caniggia but miskicked in front of goal and the chance was gone.
Arveladze decided that the direct route might prove more fruitful in 60 minutes when he burst forward and hit a left foot shot from 20 yards but it was a couple of feet too high and did not trouble Langfield.
Advocaat sent on Peter Lovenkrands for Numan 22 minutes from time, hoping he could coax the same reaction he got from the young Dane at Parkhead last Sunday knowing that a draw was not good enough.
Rangers continued to dominate the match but they could not find the goal they were looking for and it became increasingly frustrating for them.
Maurice Ross managed to beat Langfield with a header in 75 minutes when he connected with Reyna’s corner by Zhiyi was in the right place at the back post to head clear.
Mols and de Boer then came on with seven minutes remaining as Rangers fought desperately to win the game but it just would not come for the Ibrox men. The two subs came close to pulling it off when de Boer crossed the right and Mols connected with a powerful header but Langfield pulled off a great save.
DUNDEE: Langfield; Mackay, Khizanishvili, Zhiyi, Smith; Carranza (Robertson 80), Quique Torres, Rae, Ketsbaia; Sara (Milne 77), Caballero (Artero 60). Subs not used – Speroni, Gatti.
Bookings: Rae (70)
RANGERS: Klos; Moore, Konterman, Ball; Ross, Reyna, Ferguson, Numan (Lovenkrands 68); Caniggia (Mols 83), Flo (de Boer 83), Arveladze. Subs not used – Christiansen, Vidmar.
Bookings: Moore (68)
Ref: Dougie McDonald.
Att: 11,085.
Man of the match: Claudio Reyna
Moment of the match: Sadly, there wasn’t one when you consider the result.