Rangers made short work of establishing superiority, securing a two-goal lead inside the opening 12 minutes, with goals from Miller and the Frenchman Stephane Guivarc'h. Miller surged from midfield to strike his second and Rangers' third goal two minutes before the interval with a powerful drive and a similarly fierce effort from the Finn Jonatan Johansson wrapped up the scoring 14 minutes from time.
Rangers were without the suspended Colin Hendry, Giovanni Van Bronckhorst and Barry Ferguson, meaning a rare start for Miller, who wasted no Miller time in capitalising on his chance. After eight minutes, a fluent Rangers move finished with a clever lay-off by Rod Wallace into the stride of Miller, who shot powerfully across keeper Robert Douglas and into the net.
Then Albertz sent the ball down the line beyond the stretching Iain Anderson for Neil McCann, whose low cross was tapped into an empty net by Guivarc'h to put Rangers firmly in charge after 12 minutes.
At the other end a weak Eddie Annand volley was easily saved by Stefan Klos, but after 31 minutes, a surging run from Andrei Kanchelskis invited Guivarc'h to finish but he fired over from six yards. Any prospect of a Dundee recovery did disappear after 43 minutes when an Albertz ball from the right was seized upon by Miller, whose sharp finish made it 3- 0.
Dundee's misery was compounded after 56 minutes when their influential defender, Brian Irvine, was carried off with what looked a serious leg injury.
Rangers made it 4-0 within 14 minutes left when the substitute Johansson was released by an Albertz pass and scored with a fierce, angled drive.
Dundee: Douglas; Adamczuk, Irvine (Smith, 56), Anderson (Strachan, 74), Annand, Grady, Maddison, Falconer, Rae, Robertson (McSkimming, 84), Tweed. Substitutes not used: Rogers, Langfield (gk).
Rangers: Klos; Porrini, Amoruso, Kanchelskis, Albertz, Guivarc'h (Johansson, 64), Wallace, McCann, Nicholson, Vidmar, Miller (Feeney, 78). Substitutes not used: Amato, Wilson, McGregor (gk).
Referee: J McCluskey (Stewarton).