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.
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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:
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5. Quilindschy Hartman - 7/10
Defended solidly throughout and broke the lines with some purposeful balls into the forwards. Photo: Kelvin Lister-Stuttard Photo: Kelvin Lister-Stuttard
6. Josh Laurent - 7/10
Back in a more familiar midfield role and did well, spraying the ball around with confidence. Brought off relatively early to get a well-earned rest. (Photo by Michael Regan/Getty Images) Photo: Michael Regan
7. Lesley Ugochukwu - 7/10
Showed good workrate throughout and always had the better of Millwall’s midfield. Felt he had more left in the tank too. Photo: Kelvin Lister-Stuttard Photo: Kelvin Lister-Stuttard
8. Loum Tchanouna - 8/10
His goal actually came after he had started the game pretty poorly, but he was unlucky not to score a second, clipping the outside of the post. Photo: Kelvin Lister-Stuttard Photo: Kelvin Lister-Stuttard