Rangers almost got off to the best possible start when a Barry Ferguson free kick from 20 yards beat the Well wall and rebounded clear off the base of the post.
The visitors continued to dominate the early play with only Nacho Novo's shot being turned wide by Graeme Smith at his near post to show for their possession.
At the other end the home side thought they had taken the lead with their first real effort at goal but Keith Lasley's header slipped inches wide the wrong side of the post.
Within minutes Motherwell found themselves behind when Novo pounced to hammer home a loose ball which reached him after a Kris Boyd overhead kick had been blocked.
The remainder of the first half was dominated by two penalty claims. Firstly a Paul Quinn cross was handled by Ferguson in the box but to the bemusement of the home fans the free kick was given outside the box.
At the other end Novo sprinted clear of the Well defence and as he looked to gather his flick around Smith he was barged over by the keeper but once again play was waved on.
Motherwell should have been level only minutes into the second half, David Clarkson was sent clear by a Lasley through ball but with men waiting in the middle his cross was wasteful.
Rangers doubled their lead immediately after this when Novo sent Boyd clear and the striker coolly slammed the ball past Smith from an acute angle.
The visitors should have ended the tie with 15 minutes left. Novo and Ferguson combined to set up Boyd who somehow contrived to send the ball wide of an open goal.
Motherwell pulled one back as the game moved into stoppage time and Steven McGarry's corner was miss-handled by Allan McGregor and Paul Quinn was on hand to bundle home from close range.
Rangers held on and safely progressed to the semi-finals in a game which ended with nine bookings thanks to some erratic refereeing in a competitive game which was never dirty.