The decision gave Colorado a sweep of the four-game series in New York.
Mets starter Collin McHugh pitched seven innings of three-hit ball in his major-league debut and left the game with the score 0-0.
The Rockies wasted no time in getting to reliever Bobby Parnell (2-3). Colvin hit Parnell's second pitch for a triple and Chris Nelson bounced a single up the middle through the New York drawn-in infield for the game's only run.
Rex Brothers, the third pitcher for Colorado Thursday, got the win and improved to 8-2. He allowed one hit in his two innings of work.
Colorado's Tyler Chatwood pitched the first three innings, giving up three hits and walking three. Adam Ottavino followed with two innings of one-hit relief before leaving in favor of Brothers. Will Harris gave up one hit in his inning of work and Matt Belisle pitched a one-hit ninth for the third save in his nine-season career.