Gate climbed into the top 10 of the Hallmark Security League premier division with their second win in four days.
READ MORE: Runcorn Town 1 Squires Gate 2
For this visit to the struggling Manchester club, Andy Clarkson made one change to the starting side that beat high-flying Runcorn Town on Wednesday, with Jake Higham replacing the unavailable Ryan Riley.
Local youngster Jordan Salthouse was involved for the first time on the bench.
As at Runcorn, Gate started quickly and took an early lead. Gary Pett did well to battle for the ball in the corner, making his way into the box and finding Issac Sinclair at the back post to tap in his first goal for the club after two minutes.
Pett took aim from outside the box but his shot was deflected for a corner, from which Alex Colquhoun headed just over.
In heavy snow it was Gate who looked the more comfortable.
They went close again before half-time from Dan Gray’s free-kick, then Sinclair got in behind the defence and saw his cross fired wide by Pett.
Gate started the second half just as they ended the first and on 54 minutes Gray found Pett, though the striker headed straight at the keeper.
Gate doubled their lead just past the hour, counter-attacking from an Abbey corner. Seydou Bamba’s ball in from the left came back off a post for Dean Ing to head home.
The home side pulled one back six minutes from time when Daniel Hefferman fired past Fletcher, who had nothing to do until that point.
Gate’s Finley Clarkson went through one-on-one only to hit the crossbar before fellow substitute Ryan Charnley sealed victory in stoppage time.
Charnley was in the right place to tap home when Sinclair found him unmarked at the back post.
Gate: Fletcher, Gray, Rossall, Colquhoun, Higham, Sinclair, Ing, Richards, Bamba, Harries, Pett. Subs: Clarkson, Charnley, Salthouse.