First-half goals from Andy Little, Lewis Macleod and captain Lee McCulloch sealed victory as Ally McCoist's side eased home.
Rangers were boosted by the return of McCulloch after suspension and Dean Shiels from a long-term knee injury and they almost took an early lead.
Jon Daly saw a shot come back off the post after he had gathered a Lee Wallace free-kick.
But they were ahead after just five minutes when Ian Black's shot from the edge of the area was deflected off Little and evaded goalkeeper David Mitchell in the Stranraer goal.
The home side rallied but failed to turn their possession into chances, allowing Rangers to double their lead on 22 minutes.
Little crossed from the right wing, Michael Daly missed the ball in front of goal and Macleod was on hand to drill home at the back post.
The game was over as a contest on the half-hour courtesy of McCulloch, who was left unmarked eight yards out to power home a header from Law's whipped cross.
The home side did go close when Light Blues' keeper Scott Gallacher tipped over a Chris Aitken free-kick.
Rangers also began the second half well, Shiels' flicking the ball on to Daly whose shot was palmed away by Mitchell.
The afternoon then got worse for Stranraer when Aitken was dismissed on 72 minutes after picking up a second yellow card for a foul on Macleod having already been cautioned for dissent.