Gate made it eight goals in two games to record back-to-back Hallmark Security League wins at the Brian Addison Stadium.
All the goals came in the second half, Dean Ing netting two as Gate climbed a place to eighth in the premier division.
Manager Andy Clarkson handed debuts to Max Povey, a goalkeeper signed from Burscough,and Jacob Davsis, who joined the club from Kendal Town.
Gary Pett was fit enough to be named on the bench after what had looked like a season-ending injury.
Gate made a good start but were restricted to long-range shots. Billy Akrigg tried his luck but his effort was smothered by the keeper, then James Boyd shot wide.
Clarkson’s plans had to be changed before the game was 10 minutes old as Ryan Riley was forced off injured. Normally a winger, Riley had started up front but a deep gash to the knee ended his afternoon early.
New keeper Povey's first test saw him push the ball away as far as a REMY attacker, who headed over the bar.
Good awareness by Akrigg made space for Boyd but again he shot wide, then Joey Mullen fired wide from a corner.
The visitors had a good opportunity shortly before the break but the shot was curled over the top and the half ended goalless.
Gate lost their second player to injury as Pett replaced Dan Gray for the second half.
The hosts started brightly after the break as Ing fired over but REMY went closer, a long-range effort cannoning off the crossbar.
Then Gate took a grip on the game and opened the scoring on 58 minutes. Pett sprayed a lovely pass outside to full-back Joey Mullen, who took the ball forward before crossing for Ing to fire home.
Ing added his and Gate's second eight minutes later, taking hold of a bobbling ball in the area before slotting home.
REMY'S slim hopes receded further with 10 minutes left, when they had a defender dimissed for a second bookable offence.
And Gate added the icing to their cake in the last minute, when substitute Oliver Burgess did well to hold off his man before playing Ing in behind the defence, and the striker kept his composure to convert.
Gate: Povey, Gray, Rossall, Bamba, Sumner, Davis, Akrigg, Ing, Boyd, Riley, Egidi. Subs: Hargreaves, Mullen, Clarkson, Burgess, Pett.