Steven Naismith opened the scoring at Fir Park, before Kyle Lafferty doubled the advantage and Gregg Wylde wrapped up the victory late on.
The 3-0 win will no doubt act as a much-needed confidence booster ahead of Thursday's second leg against the Slovenians at Ibrox as Rangers attempt to overturn a 2-1 deficit.
Rangers were under pressure in the opening minute when Tom Hateley whipped a corner into the box for Jamie Murphy in front of goal but Allan McGregor managed to block before he could connect cleanly.
At the other end, a Steven Davis free-kick was met by Nikica Jelavic but the striker nodded just over from 10 yards out, before directing another header wide of target moments later from a Wylde corner.
The breakthrough came after 19 minutes when Davis sent a corner into the packed goalmouth and Jelavic was first to react with a bullet header that was helped into the back of the net by Naismith with the final touch.
Murphy had the ball in the back of the net after 37 minutes but the effort was disallowed after the Well player was deemed to have handled the ball before unleashing the shot.
Rangers were celebrating again on the stroke of half-time when Lafferty raced on to a pass from Juan Manuel Ortiz before sending an angled drive past Darren Randolph.
Lafferty could have added to his tally after the restart when he again combined well with Ortiz only to see his effort collected by Randolph on this occasion.
Rangers wrapped up the victory with six minutes remaining when Davis slotted into the path of Wylde and he rifled past Randolph to ensure no way back for the home side.