Delmon Young and Erik Kratz also went deep for the Phillies. Brown, the NL player of the month for May, continued his torrid hitting by going 3 for 4. He had 12 homers and 25 RBIs last month, and already has connected twice and driven in six runs in June.
Kendrick (6-3) beat the Marlins for the 12th time in 14 decisions. He lowered his ERA to 3.12 with his second complete game of the season and fourth in his career.
The Phillies trailed 2-0 before scoring three in the fifth and chasing Tom Koehler (0-4) with four in the sixth.
Kratz led off the fifth with a shot that barely cleared the wall in left-center. One out later, Kendrick ripped a liner to center and hustled into third with a headfirst dive for his first career triple. Ben Revere's RBI single tied it at 2. Revere was 2 for 21 before the hit.
Revere stole second, advanced to third on a throwing error by Rob Brantly and scored on Cesar Hernandez's RBI groundout that gave the Phillies a 3-2 lead. It was the first career RBI for Hernandez.
Brown extended the lead to 5-2 with a two-run shot in the sixth. He leads the NL with 17 homers, and certainly isn't lacking confidence.
Brown is starting to show more swagger with each drive out of the ballpark. He took a hop and skip out of the batter's box and made an exaggerated bat flip. He stutter-stepped around first base like Rickey Henderson, and exchanged a choreographed hand shake with Ryan Howard at the plate followed by a semi-bow.
The lanky left fielder has eight homers, 15 RBIs and has raised his average from .257 to .291 during an eight-game hitting streak.
Ryan Webb replaced Koehler and gave up a long homer to Young. Freddy Galvis tripled and scored on Kendrick's grounder to make it 7-2.
The last-place Marlins were coming off their first sweep of the season, over the New York Mets, and were seeking their first four-game winning streak.
They jumped ahead 2-0 in the third on RBI singles by Derek Dietrich and Marcell Ozuna.
Then, it was all Phillies.
Meanwhile, Kendrick did his job on the mound. He retired his last 15 batters.