Pinch-hitter Laynce Nix also went deep for the Phillies, who took two straight from the Mets to earn their first series win of the year.
John Buck homered for the third straight game and Lucas Duda had two solo shots for New York. The Mets set a club record by hitting at least one homer in their first nine games.
Kendrick (1-1) allowed two runs and eight hits to become the first Philadelphia starter other than Cliff Lee to get a win.
Mets starter Jeremy Hefner (0-2) gave up five runs and six hits in three innings.
A rain delay halted the game for 27 minutes in the bottom of the fourth, and strong winds and a heavy downpour late in the game left the field littered with trash during the final inning.
A night after hitting three homers off Dillon Gee in the third inning, the Phillies used the long ball in the first to jump ahead 5-0.
Jimmy Rollins hit a double after Ben Revere was caught stealing second because he overslid the bag. Utley then drove one out to straightaway center for a 2-0 lead.
Ryan Howard followed with a single and Michael Young walked before Brown launched a changeup into the first row of the second deck in right field to make it 5-0.
The suddenly slugging Phillies have six homers in the last two games after hitting four in the first seven.
Buck connected in the second for the Mets, lining a shot out to left-center. He has five homers and 15 RBIs in nine games. The Mets had five homers last season from all of their catchers -- Josh Thole (one), Kelly Shoppach (three), Mike Nickeas (one).
Duda hit a towering, 414-foot drive into the second deck in right field in the fourth to cut it to 5-2. He took Mike Adams deep in the eighth.
Kendrick pitched out of a jam in the fifth after the Mets put the first two runners on. He struck out David Wright swinging at a 2-2 changeup. After a wild pitch, Revere ran a long way to catch Ike Davis' shallow fly to left-center. Revere than threw to second base to double off Daniel Murphy.
Mets center fielder Jordany Valdespin made an outstanding shoestring catch on a shallow fly by Erik Kratz to leave the bases loaded in the third.
Nix hit a two-run shot off LaTroy Hawkins in the sixth.
NOTES: Nix has three career pinch-hit homers. ... Davis was 0 for 4 to drop to 4 for 30 this season. ... Valdespin had a career-best three hits. ... The Phillies open a three-game series in Miami on Friday night. John Lannan opposes Ricky Nolasco (0-1) in the opener. ... The Mets visit Minnesota for a three-game series, starting Friday night. Jonathon Niese (1-0) faces Vance Worley (0-1) in the opener.