Rangers 4 St. Mirren 0
Chris Burke put the home side ahead, but it was the ordering off of Will Haining on the half-hour mark which changed the course of this match.
Up until then Saints looked as dangerous as the home team, after the dismissal the visitors were torn apart. Kris Boyd and Steven Whittaker put Rangers three ahead by half-time.
The only surprise was that Rangers only added one more goal to their tally. That was a superb strike by Whittaker.
St Mirren threatened first when Billy Mehmet's glancing header had keeper Allan McGregor scrambling across his line to save. Mehmet then warmed McGregor's fingers with a powerful strike from 20 yards as the visitors controlled the early play.
Rangers went ahead with almost their first attack. Barry Ferguson turned David Barron and from his cross Burke took one touch before squeezing his shot home at the back post.
Boyd headed over Jean-Claude Darcheville's cross from only three yards before the game was over for the visitors.
Haining, who had been booked earlier for a foul on Darcheville, brought down Alan Hutton as the wing-back skipped by him and was red-carded for a second booking.
Saints keeper Chris Smith did well to save Charlie Adam's free-kick, but was helpless when Boyd shot home from 20 yards after Darcheville's clever reverse pass.
Whittaker added to Saints' woes when he drilled his shot home from ten yards after Ferguson's pass had opened up the visitors' defence.
Rangers should have added more than just one goal in the second half. Substitute Steven Naismith's pass played Boyd through, but Smith blocked well with his feet before Burke curled the rebound wide.
Boyd and Burke when close with headers before Whittaker added a fourth. Boyd's pass found Whittaker in acres of space and, after stepping inside Barron, the wing-back unleashed a powerful shot from 18 yards into the top corner.