Kendrick (5-3) allowed two runs and four hits in six innings, helping the Phillies win their second straight against the Red Sox to get within one game of .500. They haven't had an even record since they were 6-6.
Brown is doing his best to get them back there. He hit his fourth homer in three nights and leads the Phillies with 13, including an NL-high 10 in May.
"I'm seeing it pretty well," Brown said. "I'm getting good pitches to hit. After the first at-bat, I swung at a bad pitch, I told myself to wait for one to handle."
Antonio Bastardo pitched the seventh, Mike Adams struck out two in a perfect eighth and Jonathan Papelbon finished for his 11th save in 11 tries, including the second in two nights against his old team.
Papelbon allowed an RBI single to Jacoby Ellsbury, snapping his scoreless at 19 1/3 innings. But with runners on second and third, he retired Daniel Nava on a grounder to first to end it. The fiery Papelbon enthusiastically pumped his fist twice after the last out.
"A real hard-fought game," Red Sox manager John Farrell said. "The opportunities were there. They made pitches with men on base."
Nava hit a solo shot for AL East-leading Boston, which got a third straight quality start from John Lackey (3-5), who gave up six hits and three runs in six innings, but raised his ERA to 2.96.
The teams split two games at Fenway Park before moving their home-and-home, four-game set to Philadelphia.
Brown and Kratz hit consecutive homers in the fourth to put the Phillies up 3-1.
Brown then lined one out in the eighth off Koji Uehara to make it 4-2. That extra run proved important.
"He's very confident right now," Phillies manager Charlie Manuel said.
Brown had failed to live up to expectations in previous stints with the Phillies. He had an excellent spring and it has carried over.
"Just his mind-set, going out there swinging, I'm not surprised by it at all," Howard said.
Howard lined an opposite-field homer to left in the second to tie it at 1. He hadn't gone deep since May 7 against San Francisco, a streak of 61 homerless at-bats before hitting his seventh.
Nava hit an 0-2 pitch high off the right-field foul pole in the sixth. Kendrick worked out of jam later that inning, making a nice grab on Mike Carp's sharp one-hopper to start a 1-6-3 double play.
Lackey got out of a first-and-third, one-out jam in the sixth by getting Freddy Galvis to ground into a double play.
"I just had to keep making pitches and hope our guys hit a couple out," Lackey said.
The Phillies wasted another chance in the seventh when Howard struck out with one out and the bases loaded and John Mayberry Jr. popped out.
The Red Sox went up 1-0 in the first on Dustin Pedroia's sacrifice fly. Ellsbury led off with a triple on a ball that was misplayed by Ben Revere in center. Revere broke in a couple steps and had no chance to recover on the drive that landed in front of the warning track.
Pedroia acknowledged before the game that he's been playing despite sustaining a complete tear of the ulnar collateral ligament in his left thumb diving into first base in the season opener.
"I didn't expect this to come out," Pedroia said. "As players here, we all want our medical stuff to stay private. I kind of feel uncomfortable talking about it."
Pedroia is hitting .332 and has no errors while playing in all 54 games, so the injury clearly hasn't hurt his performance.
Shane Victorino, a two-time All-Star center fielder and key member of the Phillies World Series championship team in 2008, received a loud standing ovation following a video tribute. Victorino, who is on the disabled list, was traded to the Los Angeles Dodgers last July.
Injured Phillies 2B Chase Utley (oblique) and C Carlos Ruiz (hamstring) are expected to return by the middle of June, according to general manager Ruben Amaro Jr. "They're both improving," Amaro said. "We're being cautious with these injuries and thinking about the long term." ... Brown and Kratz have two of Philadelphia's five sets of back-to-back homers this season. ... The Phillies had a season-high four stolen bases. ... The Red Sox recalled OF Jackie Bradley Jr. from Triple-A Pawtucket to take RHP Alex Wilson's roster spot. ... Nava's seven homers are a career-high. ... Franklin Morales faces Phillies rookie Jonathan Pettibone (3-0, 3.21) on Thursday night. Jon Lester has been moved to Friday night against the New York Yankees and Clay Buchholz may not start until Sunday.