The Hoops took the lead after just six minutes, when Aaron Drewe’s ball over the top sent Tom Scott through, and the midfielder finished across goal for his first City strike.
Zac McEachran doubled the Hoops advantage with quarter of an hour on the clock after Corie Andrews held the ball up inside the penalty box and laid it off to McEachran, who fired past Daniel Atherton.
Drewe almost made it three just before the half-hour mark when neat play between Josh Ashby and Lewis Coyle opened up the angle for Drewe, whose shot fizzed over.
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Drewe was then on hand at the other end to make a block on the line from Connor Woods’ shot.
The hosts then made a goal line clearance when Murphy Bennett hooked away a left-footed drive from Coyle.
The Hoops searched for a third after half-time, and a passing move cut through the Warrington defence before Reece Fleet fired over the crossbar.
Scott should’ve grabbed a brace when he was teed up by McEachran, but the former fired wide with the goal gaping.
A fierce drive from Woods looked like it was going to catch out Kai McKenzie-Lyle at his near post, but the City goalkeeper made a super stop.
McKenzie-Lyle saved again deep into stoppage time to tip Josh Amis’ header over the bar and keep a clean sheet as Ross Jenkins claimed his first win back in the Hoops dugout.