Gate have lost back-to-back home games in the Hallmark Security League premier division as their wait for a first victory of 2017 continues.
Manager Danny Penswick made two changes to the side beaten by Maine Road a fortnight earlier, recalling himself and Joe Noblet, while naming new signing Curtis Haley on the bench.
Gate could have gone ahead straight from kick-off after Brett Dawson did well to cut the ball back to Jake Higham but the winger fired over.
The roles were reversed in the 21st minute, when Higham released Dawson but his low shot was cleared off the line.
Gate went close again a minute later as the Abbey keeper made a double save, first blocking another Dawson effort and then stopping Andrew Richards’ chip from the edge of the box.
Despite Gate’s mounting pressure, the visitors took the lead 10 minutes before half-time, when keeper Joe Griffith spilled the ball and Sam Noar tapped in.
The game became scrappy late in the half as Gate failed to capitalise on a series of free-kicks, but they equalised on 44 minutes with a lovely finish from their player-boss.
Penswick turned, flicked the ball up and fired into the bottom corner.
Gate had a lucky escape eight minutes after the restart, when an Abbey free-kick cannoned back of the crossbar and the follow-up shot bounced out off the underside of the bar.
Gate went close themselves from a free-kick but Noblet’s set-piece was tipped over, then Dawson’s shot was blocked in a goalmouth scramble.
The Manchester visitors regained the lead from the penalty spot on 74 minutes, though Griffith was unlucky not to stop Connor Martin’s spot-kick following a foul on the edge of the area.
Abbey fired a good chance over the top on 84 minutes but victory was secured three minutes later.
Jonathan Hardy tapped in their third, though Gate felt was ball was crossed by a player who was offside.
Gate remain 16th and Penswick said: “It was a very frustrating afternoon for us. First half we were nowhere near but second half we were the better side.
“But you can’t just turn up for 45 minutes at this level and we need to get better quickly.”
Gate travel to third-placed 1874 Northwich on Saturday.
Gate: Griffith, Carroll, Bamba, Hall, Rossall, Alexander, Richards, Penswick, Dawson, Noblet, Higham. Subs used: B.Seear, Haley, Thornber. Not Used: Moorhead, Smith.