Saints started brightly as Alan Reid went close after just five minutes, narrowly missing the target with his powerful effort.
Ryan McCay followed up for the visitors soon afterwards with a header that was cleared off the line by Sasa Papac.
With Rangers in midweek European action, Saints boss Gus MacPherson had had plenty of time to watch his opponents and the Paisley men's tactics were frustrating the home side and they seemed unable to find a way of counteracting the visitors' play.
Much of the trouble came as St Mirren moved forward quickly on the break, while Rangers were also struggling to break down their defence at the other end.
The best chance of the half for the Light Blues fell to Kris Boyd whose left-footed shot was turned around the post by Chris Smith.
Rangers started better in the second half and created several half-chances in the opening five minutes, the best of which came when DaMarcus Beasley was brought down to earn a dangerous free-kick.
As Rangers began to get numbers forward they made the breakthrough with captain Ferguson netting his third goal of the season so far on 52 minutes
Lee McCulloch chested the ball down into the path of his Scotland team-mate, who strode forward to calmly stroke his shot past Smith.
Fifteen minutes later Boyd should have doubled the lead, picking up a header from McCulloch before slicing the ball off his boot and over the crossbar. It was to be his last action of the match as Rangers replaced him with new signing Cousin.
With Rangers now fully in control of the match, David Weir forced a fingertip save from Smith, who managed to push his effort over the crossbar for a corner.
And Smith will have breathed a sigh of relief after seeing John Potter, under pressure from Cousin, knock the ball narrowly past the upright of his own goal.
On his debut Cousin sealed the win, picking up a ball from Beasley before blasting past Smith for 2-0.