Fleetwood 1 Burnley 3
(Gilchrist, Gallagher, Frost)
The Clarets came from behind with three second-half goals to secure their first win of the season in the Youth Alliance.
Jason Gilchrist, Luke Gallagher and Jamie Frost were on target for Burnley after they trailed to a first-half penalty.
Gilchrist equalised with his second goal of the season after 68 minutes when he tucked home a low cross from Gallagher.
The Clarets also hit the woodwork and went close several times before Gallagher also made it two goals in two games to put Terry Pashley's side in front.
This time substitute Lewis Nuttall created the opportunity with Gallagher beating the keeper with a smart finish as he ran into the box with eight minutes to go.
And the Clarets then wrapped up an impressive victory a minute from time when Nuttall crossed for Frost to head in at the far post.
Burnley: Jakovlevs, Azam, Whitmore, Obebi, Hill, Jackson (Nuttall 72), Lowe (Bianga 74), Daly, Frost, Gallagher, Gilchrist. Subs: Holt, Barnes, Hasler-Cregg