A week on from revealing how "ashamed" he was at a plane carrying the message 'White lives Matter Burnley' over the Etihad Stadium during the club's 5-0 thrashing to Manchester City, the defender was impressive throughout in south London.
Mee ended his three-year wait for a goal with a header in the 62nd minute and it sealed a 1-0 win to move Sean Dyche's men up to eighth in the Premier League.
Palace, despite enjoying the better of the contest in the second half, could not respond and suffered a second consecutive defeat.
Ashley Westwood's corner was only partially cleared and traditional winger McNeil drilled over from inside the area.
The Burnley number 11 was on the charge again a minute later, but could only fire tamely at Vicente Guaita, who was back after a thigh problem.
Before the first half ended there was an exchange of words between Zaha and Burnley assistant Ian Woan, with the former telling the opposition coach to "sit down" which added extra spice to proceedings after the break.
It would prove costly for the Eagles as Burnley took the lead in the 62nd minute when Westwood's free-kick found captain Mee, and he stooped low to head home from 14 yards.
Guaita would have been disappointed after getting a hand to the effort, but the ball hit the post and rolled in to give the Clarets defender his first goal since January 2017.
Palace, who enjoyed the better of the game after the break, upped the ante and Andros Townsend, Zaha and Ayew all had efforts, but the visitors, aided by Mee's heroics, stood firm to make it back-to-back 1-0 wins.