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.
In the fact, the best chance of the half only came in the 41st minute, but Harrison Biggins could only fire agonisingly wide for the Trawlermen after breaking into the box.
The start of the second 45 minutes promised more, particularly for the Reds.
A brilliant Danny Ings solo run almost provided a goal moments after the restart, before slick link-up play between Bobby Adekanye and Ovie Ejaria resulted in both men seeing shots blocked.
But the Reds' frustration prompted Critchley to look to his substitutes once more, calling on a man who has regularly made an impact from the bench this season in Matty Virtue.
And just four minutes later he was rewarded as the midfielder played a key role in the move that ended in Johnston smashing home from inside the box.
With opportunities proving hard to come by in the aftermath, it looked like Liverpool were set for a comfortable end to proceedings.
But with five minutes remaining, Soweby produced a brilliant curler that gave Kelleher no chance and sparked a lively end to the game that saw Bobby Adekanye have an effort headed off the line.
In the end, though, neither team could find the winner, meaning the destination of the trophy would be decided by the lottery of penalties.
And Kelleher subsequently proved to be the hero for Critchley's men, making a decisive stop from Fleetwood's first penalty taker to win the trophy for Liverpool.
Liverpool: Kelleher, Whelan, Parker, Masterson, Johnston, Ejaria, Coyle (Virtue, 69), Alves, Wilson (Adekanye, 45), Dhanda, Ings.
Unused subs: Firth, N. Phillips.