Both sides were evenly poised at the break but the Clarets - who made 10 changes around the hour mark - edged back ahead on 72 minutes through Dan Agyei, who applied the finishing touch to Jonathan Walters's cross.
This time, North End would respond with a quick equaliser as Callum Robinson found the bottom corner from close range just two minutes later.
Just as it seemed like neither side would claim victory, 18-year-old McNeil was the hero for the Premier League side as he volleyed home from just outside of the box.
BURNLEY: Heaton (Legzdins 46'), Lowton, Tarkowski, Mee, Ward, Gudmundsson, Cork, Westwood, Lennon, Hendrick, Vokes
Substitutes (all on the hour): Taylor, Koiki, Benson, Goodridge, Walters, Wells, Bardsley, Long, McNeil, Agyei, Dunne, Younger
PRESTON NORTH END: Rudd, Woods (Fisher 70'), Huntington, Storey, Hughes, Pearson (Ledson 60'), Johnson (Moult 70'), Harrop (Browne 70'), Burke (Bodin 63'), Robinson, Maguire (Horgan 80')