Former York winger Matty Blair's winner in Monday's first leg of their semi-final proved enough for Graham Alexander's side to reach Wembley.
Both teams began the match at the Highbury Stadium in cagey fashion, but the hosts had the first attempt on goal in the fourth minute.
Josh Morris blazed over the bar, before York captain Russell Penn did the same at the other end shortly after.
In an end-to-end contest that had few clear-cut chances, it was Fleetwood who nearly broke the deadlock midway through the second half.
Midfielder Antoni Sarcevic's low effort was saved well by York keeper Nick Pope.
Despite a nervy final 10 minutes, Alexander's men held on and will now face either Southend United or Burton Albion in next week's final with a place in League One at stake.
