The Minstermen started the game where they had left off at Aldershot at the weekend, with both Matty Blair and Jamal Fyfield testing Scott Davies before Michael Coulson struck the bar.
After riding their luck for the majority of the first half, the visitors opened the scoring with their first effort on goal in the 35th minute through Junior Brown. The winger produced a spectacular effort from distance to find Michael Ingham's top corner via the slightest of deflections at Bootham Crescent.
Just past the hour mark, it looked as if the visitors would give themselves a two-goal cushion as David Ball rounded Ingham only to see his effort cannon off the post before Jamie McGuire's follow-up was blocked on the line.
With three minutes remaining, substitute Steven Gillespie sealed the win for Fleetwood as he got on the end of Brown's flick-on to calmly slot past Ingham.
