Burnett (6-4) threw 108 pitches, 64 of them strikes, walked three batters and fanned 10.
Relievers Brian Bruney and David Robertson hurled one scoreless inning apiece.
Jorge Posada's only hit of the game was a game-breaking three-run homer in the top of the sixth inning following an RBI single by Alex Rodriguez.
Nick Swisher hit a third-inning solo homer, while Melky Cabrera added two hits for the Yankees, who will try to sweep the Subway Series Sunday.
The Yankees went 2-for-5 with runners in scoring position and stranded seven base runners.
Alex Cora's sixth-inning lead-off single was the lone hit for the Mets, who have split their last six games.
Losing pitcher Tim Redding (1-3) yielded five earned runs and six hits in 5 1/3 innings with two walks and six strikeouts.
Celebrity Families of 2014 [PHOTOS]