Ashley Barnes was at the double as Scott Parker’s side put their Championship opponents to the sword to claim their first win since October.
Loum Tchaouna, Jaidon Anthony and Jaydon Banel also got in on the act during their one-sided 5-1 win.
The Burnley Express has launched a new WhatsApp channel to bring the latest news, analysis and team & injury updates directly to your phone. Simply click this link to join our Burnley Express WhatsApp channel.
Josh Coburn grabbed a late consolation for Alex Neil’s side, put that failed to take any gloss of what was a dominant display from the Clarets.
Here’s how Burnley’s players rated:
Your next Burnley FC read: Scott Parker outlines why second loan move was right 'solution' for Burnley's Luca Koleosho
13. SUB: Hannibal - 5/10
For Ugochukwu, 65 Picked up a silly booking and got caught in possession for Millwall’s late consolation. (Photo by Molly Darlington/Getty Images) Photo: Molly Darlington
14. SUB: Jaydon Banel - 7/10
For Bruun Larsen, 78 Slammed home from close range to score his first Burnley goal. (Photo by Matt McNulty/Getty Images) Photo: Matt McNulty