Charlie Austin scored late in the first half to give Burnley a 2-1 lead over Millwall heading into the break at Turfmoor this afternoon.
The hosts fell behind after just three minutes when Liam Trotter played the ball out wide to Andy Keogh, before collecting the return pass and firing in from the edge of the box.
Ben Mee levelled the scores on 19 minutes when he headed in Junior Stanlisas's corner for his first Clarets goal.
Burnley were angered when their appeals for a penalty were turned down, despite Danny Shittu appearing to handle the ball in the box.
Austin completed the first-half turnaround when he climbed to powerfully head in Kieran Trippier's inviting 43rd-minute cross.
It was the former Swindon Town striker's 11th goal of the season, making him the country's leading scorer in all competitions.