It was testimony to their shaky performance that Allan McGregor was named man of the match and their keeper made at least four point-blank saves to keep out the Norwegians.
Rangers had the cushion of an early goal by Thomas Buffel, but it took Barry Ferguson's strike on the stroke of half-time to calm the home team's nerves.
Once again the centre of the Rangers defence looked weak, with Julien Rodriguez and Brahim Hemdani failing to convince.
Rangers took the lead when Dado Prso 's pass found the advancing Steven Smith and from the wing-back's cut back Buffel reacted first to touch the ball home at the near post.
Molde then passed up a marvellous chance to equalise when the totally unmarked Marel Baldvinsson somehow headed wide from six yards.
McGregor then produced a finger-tip save to keep out a Magne Hoseth header.
It was just as well for Rangers that they scored their second goal just before the interval with the best move of the match.
Smith's crossfield pass was well controlled by Libor Sionko and from his pass Kris Boyd backheeled the ball into the path of Ferguson, who dispatched his shot low into the corner of the net.
If Rangers though that would end Molde's resistance they were mistaken.
Early in the second half Hoseth outpaced Hemdani, but once again McGregor came to Rangers' rescue.
The keeper than produced another marvellous block to keep out Baldvinsson as Rangers were content to run down the clock.