The visitors collected all three points in rather unconvincing fashion against Jim Duffy's depleted Dundee side.
Rangers started brightly and Julian Speroni saved Robert Malcolm's shot before David Mackay cleared Peter Lovenkrands' effort off the line with just three minutes gone.
The visitors did take an early lead when Nuno Capucho headed Chris Burke's right-wing cross past Speroni from four yards with six minutes gone.
Dundee captain Barry Smith saw two efforts well saved by Stefan Klos as the home side tried to hit back.
Midway through the first half Nacho Novo ran past two Rangers defenders before hitting a low drive goalwards from 18 yards which forced Stefan Klos to save at full stretch.
Novo went close again with half an hour gone but was denied by Klos.
Five minutes later Rangers went two up in a rather strange fashion.
Michael Ball's free-kick from 35 yards was floated to the back post and was missed by everyone and ended up in the corner of the net.
Lee Mair almost pulled the home side back into the game just before half-time, but his right-foot shot crashed back off the post.
A minute after the interval Lovenkrands saw his left-foot strike come back off the other post after collecting a super pass from Mikel Arteta.
Dundee youngster Robert Linn was set up just inside the box by Novo, but took too long to get a shot in and was crowded out by the Rangers defence.
With six minutes left a long ball from Barry Smith was just too strong for Novo and Klos gathered.
Rangers sub Paolo Vanoli should of made it three in the last minute, but with only the keeper to beat and standing in acres of space, he hit the ball straight at Speroni and the match ended 2-0.