John Coleman's side were always in charge at Stonebridge Road, with Andy Todd's first goal for the club and a Paul Mullin double earning a comfortable win, with Fleet's lone replay a late Ross Smith consolation.
The home side started brightly with Mark Rawle showing up well in attack, but they were unable to break down a resolute Reds backline.
They were made to pay just after the half-hour mark as Gary Roberts' left-wing corner was headed in by Todd, who only recently joined Stanley on loan from Burton Albion.
Soon after half-time, visitors keeper Rob Elliot parried away a Smith header from Andy Drury's corner and a few minutes later Mullin pounced to double the lead.
Drury tested Elliot with a 20-yard effort with 20 minutes left to play, but eight minutes later the game was over as a contest as Mullin scored his second of the evening, converting a pass from Roberts.
Fleet eventually gained some reward for their efforts with time running out as Smith headed home Robert Watkins' corner, but it was nowhere near enough to derail Stanley's title ambitions.