For all their dominance, the home side would have been level at the break had it not been for a diving two-handed save from Thomas Pamment, who sent a rare Warkworth shot off his bar and away from trouble.
Prolific goal scorer Jack McNab had a double midway through the half to extend the score to 3-0.
The first came from a simple tap in from close range after a quality ball across the box from Mark Knell, while the second was of real quality.
A beautiful cross from Stephens landed smack on the forehead of a free McNab at the back post, opening the way for more goals as Warkworth lost shape and began to break down.
Stephens showed what a pivotal addition he has been by nodding home a well-taken header to make it 4-0, leaving only a loosely-marked McNab to pick up his hat trick to take the score out to 5-0.
The win keeps City in fifth place on the ladder with plenty of momentum heading into the competition's closing stages.
Meanwhile, Tauranga Old Blues stayed in the hunt in Federation One with a 4-1 win away over Melville United.
Tauranga City 5 (Jack McNab 3, Craig Stephens 2) Warkworth 0