Kendrick (2-1) struck out five and walked one while throwing 107 pitches. His only other shutout came last season, during which he went 11-12 for the Phillies.
The game was scoreless through five innings, but Philadelphia broke things open with a four-run sixth.
The Mets had no more than one base runner in any inning while losing their second in a row. Philadelphia ended a three-game skid.