It took Rangers a while to warm up, but when they did the home side struck with devastating effect.
A closely fought first half ended with Mikel Arteta curling in a magnificent free-kick.
In a brilliant ten-minute spell after the restart, goals from Maurice Ross, Hamed Namouchi and Steven Thompson blew aside the visitors, who ended up grateful they did not suffer a heavier defeat.
Rangers threatened first when Namouchi's superb crossfield pass found Chris Burke who worked his way along the by-line, but no-one was there for his cutback.
Thompson then headed narrowly wide from another Burke cross.
Paolo Vanoli just managed to block Jason Dair at the last minute as the Motherwell midfield player was poised to shoot from Dave Clarkson's pass.
Thompson was then adjudged to have pulled back Steve Craigan as he advanced on goal after chesting down a superb Frank de Boer pass.
Fernando Ricksen's pass reached Burke, but the winger's left-foot shot was straight at Gordon Marshall.
The Motherwell keeper then nearly cost his side dear when he spun a clearance high into the air, but redeemed himself with a good block from Namouchi.
Steve Craig should have done better for the visitors when he broke clear on the left, but his shot hit the sidenetting when a cross might have been the better option.
Ricksen and Alan Hutton were then booked as the game threatened to boil over.
Arteta was fouled just outside the area by Craigan but Well were made to pay when the Spaniard curled the free- kick high into the top corner with Marshall only able to get a despairing hand to it.
After the break, Ross scored his first goal of the season when he latched on to a superb Burke pass before shooting home much to his delight.
A classic throughball by de Boer released Namouchi who shot low under Marshall to put the home side three ahead.
Arteta's pass found Vanoli on the left and the wing-back's cross was met with a glancing header from Thompson which left Marshall stranded.
The home team could have added to their tally with Stephen Hughes going close and Ricksen testing Marshall with a long-range effort.