George Johnston's second-half strike looked to have won a hard-fought game for Neil Critchley's side, but they were taken to a shootout by Jack Soweby's stunner just five minutes from time.
That late concession couldn't stop the Reds from clinching victory, however, with Caoimhin Kelleher producing a fine save from former Everton man Michael Donohue to seal a 5-4 shootout win.
With a trophy on the line in Leyland, the teams played out a cagey start to proceedings, with chances at a premium in the early stages of the first half.
The returning Harry Wilson and Fleetwood forward Donohue both managed to get shots away in the opening 20 minutes, but neither player truly tested the goalkeeper with their respective efforts.