Cowgill's seventh-inning home run completed the day's scoring and made him one of six Mets batters to have two hits Monday. New York battered five Padres pitchers for 13 hits and also drew five walks.
Mets starter Jon Niese (1-0) allowed four hits and two runs in 6 2/3 innings and three relievers followed with a total of 2 1/3 innings of no-hit relief.
Niese was one of the Mets with two hits, including a run-scoring single after Ruben Tejada's RBI double in the second. After San Diego scored a third-inning run on Carlos Quentin's base hit, New York answered with RBI singles from Marlon Byrd and John Buck in the bottom of the inning.
The Mets, who chased San Diego starter Edinson Volquez (0-1) after three-plus innings and six runs, broke the game open with three-run rally in the fourth that Niese opened with a walk and Byrd finished off with a single.
Yonder Alonso hit a home run to open sixth for the other San Diego run.
Cowgill's grand slam was on a line smash over the left-field wall.