Rangers 3-1 Dundee
Arveladze celebrates the first of his two goals
Rangers left it late to secure all three points against an unlucky Dundee side.
After a goal-less first half, Rangers took the lead through Shota Arveladze.
But Dundee came storming back and looked like they might have earned a point when Nacho Novo equalised.
But in the dying minutes, Paolo Vanoli scored a fabulous goal and then Arveladze made sure of the victory.
Rangers enjoyed the bulk of the early pressure without really threatening the Dundee goal and it was 12 minutes before Julian Speroni was called into action.
Mikel Arteta curled a free kick from the angle of the penalty area towards the top corner, but the keeper was equal to it.
Moments later Michael Mols should have scored from close range after Maurice Ross had picked him out, but the Dutchman's effort was lazy and trundled wide.
Dundee began to come into the game, with Fabian Caballero and Gavin Rae causing problems and Stefan Klos gathered the ball after Henning Berg's challenge ricocheted off Rae.
Peter Lovenkrands spurned an excellent opportunity after being released by Mols, but the Dane's shot from 12 yards out was well off target.
Dundee had a terrific chance to open the scoring six minutes before half time when Nacho Novo was sent in on goal, but he struck his shot straight at Klos.
Nuno Capucho tested Speroni from a tight angle, although a better option might have been to cut the ball back for Mols or Shota Arveladze.
Paolo Vanoli scored a fantastic goal
Dundee suffered a setback at the beginning of the second half when Brent Sancho was stretchered off after a challenge on Arveladze and Juan Sara came on as a replacement.
Novo tested Klos again, this time from long range, but the German held the ball comfortably.
The breakthrough for Rangers finally came after an hour.
The build-up was scrappy, with the ball bouncing around in the box before Lovenkrands knocked the ball to Mols, who headed to Arveladze and the Georgian volleyed past Speroni.
Dundee refused to cave in though and Caballero tested Klos with a fierce drive from a narrow angle and then the keeper did superbly to tip Sara's header round the post.
Caballero fired another effort just over but Rangers finally seemed to weather the storm.
However with just under quarter-of-an-hour remaining, Dundee pulled level when Sara headed into the path of Novo who fired past Klos from close range.
Mols passed up two good opportunities inside a minute as Rangers stepped up the pressure again.
That paid off when a ball into the box was only cleared as far as Vanoli who drilled a 25-yard shot into Speroni's top corner with only four minutes remaining.
Two minutes later the game was over as a contest as Arveladze headed past Speroni after terrific work from Capucho.
Rangers: Klos, Ross (Hughes 77), Berg (Moore 45),
Khizanishvili, Ball, Emerson, Arteta, Capucho,
Lovenkrands (Vanoli 71), Mols, Arveladze.
Subs Not Used: McGregor, Ostenstad.
Dundee: Speroni, Mackay, Wilkie, Mair, Sancho (Sara 53), Smith,
Nemsadze, Rae, Cowan, Novo (Hutchinson 88), Caballero.
Subs Not Used: Langfield, Fotheringham, Hernandez Santos.
Booked: Mair, Rae.
Ref: W Young