The Whites broke the deadlock against the Clarets inside seven minutes, with Dennis Politic cutting in from the edge of the box and firing into the roof of the net from 15 yards out with his left foot.
That advantage was then doubled three minutes later through Connor Hall, with him collecting a superb ball from Jeff King before scoring from a narrow angle ten yards out.
The home side did halve the deficit on the 20 minute mark through Tinashe Chakwana who swept home a Dean Marney cross, but Bolton's two-goal advantage was restored five minutes before the end of the first half as King turned goalscorer who beat his man and sidefooted home from nine yards out.
Having looked dangerous throughout the first period, the Trotters' determination continued in the second period and they were rewarded with a fourth through Liam Edwards in the 82nd minute who defended the first ball before scoring from all of 40 yards, lobbing the Burnley keeper in the process to put a gloss on the result for Wanderers.
Speaking following the final whistle, David Lee said, "It was a hugely pleasing result for us. Burnley had an experienced player in Dean Marney on their side, but our lads' desire and attitude was brilliant.
"Their attitudes were spot on and the manager came into the changing room after the match to praise them for their efforts.
"We thoroughly deserved the win and even had two Under-18s in Shakeel Jones-Griffiths and Dennis Politic in the team which was a great experience for them.
"Overall, we couldn't have asked any more of the lads. To beat a Premier League team is no mean feat and the players should be very proud of themselves."
Bolton: Turner, Brockbank, Lonsdale, Edwards, Mitchell, Jones, Politic (White 80'), Earing (Perry 70'), Hall (Trialist 80'), King, C Taylor
Subs: Aspinall, Perry, White, Moulden, Trialist