Cue Paolo Vanoli. The Italian defender-cum-midfielder had only been on the field for around 16 minutes as a substitute when he unleashed a venomous shot from around 30 yards that darted into the top corner to once more give the Light Blues the lead.
With Ibrox still celebrating, Shota Arveladze then grabbed his second of the game to effectively end any chance of another Dundee comeback.
While Alex McLeish will be delighted with the victory, he may have some concerns about the laborious way his team fashioned out the result.
Rangers had gone into this match on the back of a comprehensive 4-0 thumping of Hearts the previous weekend but seemed unable to re-capture that sparkle as they struggled to find a way through a well-marshalled Dens Park outfit.
There seemed a lack of urgency from the Light Blues at times, as if it would be only a matter of time before Dundee’s defiance evaporated and they succumbed to the inevitable.
Despite enjoying the lion’s share of the possession, there were few clear cut chances for the Light Blues in a hesitant first half performance.
Mikel Arteta curled in a free kick that was easily held by Julian Speroni before Michael Mols slid a chance wide from close range in the opening exchanges.
Emerson was again looking lively in the heart of the midfield and his chipped pass released Shota Arveladze after 21 minutes but the Georgian snatched at the chance, sending it spiralling high into the stand.
Rangers seemed to want to walk the ball into the box and Arveladze passed up a great chance just six yards out, trying a difficult pass to Mols when a shot seemed the better option.
Even without new capture Fabrizio Ravanelli – not yet match fit – Dundee looked consistently dangerous on the counter-attack, with Fabian Caballero in particular a potent threat up front.
Nacho Novo fired a long-range attempt over the crossbar after 17 minutes and then shot straight at Stefan Klos after latching on to Georgi Nemsadze’s searching long ball 20 minutes later.
The eccentric officiating of Willie Young only served to add to the frustration gathering around Ibrox, with the referee making some baffling decisions against both sides.
Skipper Craig Moore made his comeback from injury at the start of the second half, replacing Henning Berg, as the Light Blues continue to press forward looking to break the deadlock.
The first chance of the half, however, fell to Dundee when Gavin Rae raced 80 yards up the field to release Nemsadze whose shot was well saved by Klos.
Relieved by that let-off, the Light Blues belatedly went in front just short of the hour mark.
Peter Lovenkrands’ lofted pass was headed down by Mols for Arveladze to execute a trademark swivel and volley into the roof of the net.
Dundee, to their credit, refused to buckle and only a stunning stop from Klos denied substitute Juan Sara before the lively Novo grabbed an equaliser on 76 minutes when he converted from close range.
With Rangers’ 100 percent league record in danger of expiring, the stage was set for Vanoli and his thunderous shot from 30 yards flew into the top corner of the net, leaving Speroni grasping at thin air.
To compound Dundee’s misery, the Light Blues netted a third in the closing stages. Nuno Capucho turned former Gers defender Tom Cowan inside-out before crossing for Arveladze to head home.
RANGERS (4-4-2): 1 Klos; 21 Ross (Hughes 76), 25 Berg (Moore 46), 15 Khizanishvili, 18 Ball; 20 Capucho, 4 Emerson 23 Arteta, 26 Lovenkrands (Vanoli 70); 7 Arveladze, 10 Mols
Subs not used: McGregor, Ostenstad
Booked: None
DUNDEE (4-4-2): 1 Speroni; 3 Mackay, 6 Wilkie, 19 Mair, 23 Cowan; 18 Sancho (Sara 52), 2 Smith, 10 Nemsadze, 8 Rae; 17 Novo (Hutchison, 86), 7 Caballero
Subs not used: Langfield, Fotheringham, Hernandez
Booked: Mair (67), Rae (69)
Man of the Match: Zurab Khizanishvili