Alan Fettis was still missing because of a dead leg, so juniors custodian Danny Harvey started in goal. Justin Whittle and John Anderson were at the heart of the defence, while forwards Daniel Webb and Clayton Donaldson were staking their claims for a first team place.
Alex Taylor headed past Harvey after 25 minutes from Luke Chadwick's cross, but City were back on level terms before half time as Danny Pitham deflected Webb's cross into his own net.
Donaldson put City 2-1 ahead after the break, but Chadwick's free kick levelled matters again.
The winger on loan from Manchester United then got the winner in the 70th minute, firing in at the back post to secure a 3-2 win for Burnley.
City line-up: Harvey; Regan, Whittle, Anderson, Peat; Russell, O'Neil, Keates (Tomlinson 73), Holt; Webb, Donaldson (Matthews 78).