Despite Rangers' dominance, the visitors ended up taking the lead in the 27th minute, when Lee Erwin cut in from the right and let fly with a shot that bounced off Darren McGregor and into the net past goalkeeper Cammy Bell.
Motherwell then shocked the home crowd by doubling their lead five minutes before half time, Marvin Johnson lashing in a free kick from the right and Stephen McManus steering a powerful header into the corner of the net.
It would get even worse for the hosts as the relegation-troubled Scottish Premiership side added a third shortly after the restart, courtesy of Lionel Ainsworth's low shot from the edge of the penalty box.
Rangers appealed for a penalty five minutes later when a ball deflected off Marvin Johnson's knee and onto his arm, but referee Bobby Madden gave nothing.
There was, however, some solace for Stuart McCall's side ahead of the second leg as, in the 82nd minute, Nicky Law's ball was emphatically nodded home by McGregor.
Despite a last foray by Rangers, including a Kris Boyd strike that was disallowed for offside, the final whistle blew with Motherwell firmly in the driving seat ahead of the return meeting at Fir Park. body check tags ::