Millwall had a dream start. Ivanovic darted to the front post in front of CJ Egan-Riley to meet George Honeyman’s cross after clever hold-up play by Josh Coburn.
But Burnley hit back instantly through Brownhill. He fired home with a low, emphatic finish into the bottom right corner after Ashley Barnes charged down Jake Cooper’s clearance.
Brownhill forced George Evans into a strong save with a strike from distance after 25 minutes, as the home side looked to go ahead on a frantic day of drama.
Millwall’s Coburn put forward a contender for miss of the season 10 minutes before the break, hitting the post just yards out from an open goal after being found by Tristan Crama’s low cross.
Burnley looked to force the issue early into the second half through Hannibal Mejbri’s curling strike, which whistled over the bar, and efforts from Anthony and Marcus Edwards, both blocked by Evans.
But it felt as though a second goal was coming, and Anthony was Burnley’s driving force. On 65 minutes, he completed the turnaround with a wonderful first touch and finish inside the area.
Ivanovic failed to connect with a header as another gilt-edged chance went begging, before Cooper was denied by James Trafford as Millwall looked to salvage their dwindling Premier League dream.
Scott Parker’s home side survived incredible late pressure before getting their third goal, but the day ultimately ended in disappointment having come so close to glory.