New York was facing a 2-1 deficit when Byrd smacked his 12th home run of the season after Daniel Murphy had reached on a one-out single.
The Mets concluded an unusual four-city road trip with a 7-4 record. The journey began with five games in Atlanta and ended with a lone outing in Denver, a contest that made up for a game rained out in April.
LaTroy Hawkins (3-1) collected the win by working the seventh inning in relief of Jeremy Hefner.
Scott Rice came on in the eighth and escaped problems despite giving up two hits and throwing a wild pitch. Bobby Parnell picked up his 14th save, avoiding potential difficulties when leadoff man Michael Cuddyer was thrown out at second trying to stretch a single.
Byrd's homer came off Matt Belisle (4-5).
2014: The Year in Music [PHOTOS]