Rangers barely had to move out of second gear to record their first league win of the season.
First-half goals by Peter Lovenkrands, Michael Mols and Mikel Arteta put the champions on Easy Street. Arteta added the fourth after the break.
Kilmarnock's cause was hardly aided by the foolish dismissal of Chris Innes in the 34th minute for repeated fouls on Mols, especially as the centre-back had previously been booked in the fifth minute.
In a low-key start Lovenkrands saw a flashing shot blocked before Rangers took the lead with a bizarre goal.
From Fernando Ricksen's cross Killie keeper Colin Meldrum appeared to have caught the cross confidently, but after bumping into his own player he spilled the ball in front of Lovenkrands, who was left with a simple tap-in.
A minute later the home side were denied by a close offside decision as Ronald de Boer swept home a Lovenkrands cross after a surging run by Barry Ferguson.
After Innes' departure Rangers soon added to their lead from Arteta's corner. Craig Moore headed down before Mols swept the ball home off a Killie defender.
The visitors' woes increased when Sean Hessey and Greg Shields were guilty of blocking Ferguson as he advanced on to a de Boer cross. Arteta converted the resultant spot-kick easily.
Rangers stepped up the pressure early in the second half against ten-man Kilmarnock and Meldrum did well to hold a Ferguson drive.
Michael Ball received a standing ovation for his efforts as he was replaced by Paolo Vanoli and it was the substitute who nearly created the Gers’ fourth with a cross that somehow eluded Mols.
The home side's next goal was not long delayed. Arteta collected a cross by Lovenkrands before drilling a magnificent shot low into the corner from 22 yards.
Mols nearly added a fifth in the last minute, but pulled his shot wide. Rangers will surely face a tougher task against FC Copenhagen on Wednesday in the Champions League qualifier.