The holders took the lead after only 75 seconds through Andrius Velicka and once Kris Boyd netted the second just after the hour mark, it was all over for the Saints.
Substitute Kenny Miller added the third for the Gers, whose only black spot was seeing midfielder Pedro Mendes stretchered off just before the interval.
Rangers took an early lead with a well-crafted goal. Steve Smith did well to switch play to Steve Davis, whose pass into the box found Boyd.
The striker's shot was blocked by Will Haining it fell to Velicka who shot high into the net from six yards.
Mendes then tested the Saints keeper with a curling effort which Mark Howard turned away for a corner.
Saints recovered well from the poor start and kept possession without really threatening the Rangers rearguard. Indeed, their only effort of note in the first half was a powerful 25-yard shot from Steve Thomson which Neil Alexander tipped over.
A strong challenge from Haining on Mendes led to the Portuguese player being stretchered off, before Rangers should have added a second. Davis rolled his pass into the path of Velicka, but the striker sliced his shot wide.
After the break, Steven Whittaker produced a magnificent tackle to take the ball from Andy Dorman in the box before Rangers scored a crucial second.
Again it was Davis from midfield and his perfectly-weighted pass released Boyd, who made no mistake with his left-foot shot for his 100th goal for Rangers.
For their third goal, Davis released Nacho Novo whose cross was headed down by Boyd for Miller to squeeze his effort home.
Saints tried for a consolation goal, but never carried any real threat in what was a disappointing effort from the underdogs.