The visitors capped off a bright start when taking the lead in the 22nd minute as Gareth Evans headed home unmarked at the back post after Michael Ingham could only parry Jamille Matt's header.
Minutes after the goal, Fleetwood nearly doubled their lead with Ingham dropping Jeff Hughes' cross at the feet of Matt but he quickly gathered the ball at the second attempt.
York were finding it hard to create any real openings, with Luke O'Neill and Lewis Montrose both forced to try their luck from range.
After the restart York had claims for a penalty waved away after top scorer Ryan Jarvis tumbled under the challenge of Ryan Cresswell in the area.
Graham Alexander's team then sealed the points in the 66th minute as Matt reacted quickest in the area to fire home after Ingham could only palm away Steven Schumacher's curling free-kick.