Lincecum (1-2) yielded one run on four hits and overcame five walks for the Giants, who won the make-up game of a contest postponed by rain Sunday.
Nate Schierholtz went 3-for-4 with a three-run homer and a triple while Buster Posey added a solo shot as San Francisco won for the seventh time in 10 games.
The Mets started Miguel Batista (0-1) for the first time this season, and the hurler was tagged for six runs (three earned) on seven hits and three walks over a 3 2/3-inning effort.
Mike Baxter drove in the only run for New York, which fell for the fifth time in seven contests.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys