A second-half hat-trick by Kris Boyd on his Rangers debut ensured there was no upset at Ibrox.
Sotirios Kyrgiakos had put the home side ahead at half-time, but once Boyd had scored his first goal from the penalty spot early in the second half there was no way back for Peterhead.
Substitute Ross McCormack curled home a superb shot to make it five for the home team.
The visitors survived the first-half barrage with keeper Paul Mathers making a string of superb saves.
Twice the Peterhead keeper blocked efforts from Peter Lovenkrands when the Danish striker was through on goal.
Mathers also did well to hold a powerful drive from Nacho Novo and to touch over a Boyd header before Rangers finally made a break-though in the 34th minute.
Novo's header from a Lovenkrands cross struck Boyd, who turned and shot against the post, but Kyrgiakos was able to force the ball home from close range.
Lovenkrands' run early in the second half was blocked by Craig Tully, and referee Brian Winter awarded penalty. It looked a soft award, but Boyd stroked home the spot-kick.
It was not long before the striker added his second when he headed home Novo's cross. Boyd then completed his hat-trick when he powerfully headed home a superb cross from Alan Lowing.
It was another substitute, McCormack, who completed the scoring with a superb strike from Novo's pass.
Peterhead were not disgraced but in the end it was a comfortable win for the home side.