Kendrick (4-4) allowed one run and five hits over seven strong innings to help the NL East-leading Phillies win their fifth straight game.
"I want to start," he said. "It's their decision."
Kendrick has mostly been used as a starter since his rookie year in 2007. He spent most of 2009 in the minors, bounced back to win 11 games in 31 starts a year ago and then was bumped to long relief at the start of this season.
Filling in for injured right-hander Joe Blanton, Kendrick had his sharpest outing of the season.
"He draws a lot of criticism at times, but he's been a winner," Phillies manager Charlie Manuel said.
Rollins and Valdez had their big hits in a six-run third inning against Marlins starter Elih Villanueva (0-1). Villanueva threw 92 pitches and lasted three innings in his major league debut for the Marlins, who lost their fifth straight. After the game, the Marlins optioned Villanueva to Triple-A New Orleans
Rollins went deep for the second straight game and had four RBIs. The Phillies are a season-high 16 games over .500 at 42-26 -- the best record in baseball.
"I like when we're playing good," Manuel said.
The Phillies wasted little time rocking a jittery Villanueva. They led 2-1 in the third when the righty unraveled. He hit Chase Utley and walked two batters, loading the bases for Valdez.
Valdez is known more for being the winning pitcher in a 19-inning game than anything he's done at the plate this season.
He had only nine RBIs in 147 at-bats when he hit the ball deep to left-center. Florida left fielder Logan Morrison missed his stab at it and went tumbling, almost colliding with Chris Coghlan. Coghlan landed face-first on the warning track dirt, allowing Valdez to scoot to third for the triple.
"I was running hard whether they were going to catch it or not," Valdez said.
Rollins homered three batters later, his sixth homer landing in the first few rows of the right-field seats. That made it 8-1 -- and the Marlins had no one warming in the bullpen.
Villanueva finished the third and that was it for Florida's 2010 minor league pitcher of the year (14-4, 2.26 ERA).
"We need consistency on the mound, a starter that can keep us in the game," Marlins manager Edwin Rodriguez said. "We haven't showed much offensively so we're putting a lot of pressure on the pitcher."
Kendrick, who was bounced to the 'pen earlier this year, pitched more than five innings for the first time this season. He allowed Morrison's two-out solo homer in the first but then retired 14 of 15 in one stretch. He allowed four singles and walked none after the homer.
Blanton isn't expected back for another month, leaving Kendrick and Vance Worley competing for the fifth spot in the rotation.
"Everybody wants things to work out perfectly, but this game's not like that," Kendrick said.
Ryan Howard tied it in the first with an RBI double that scraped the right-field foul line, and Rollins' single to right in the second made it 2-1. The Phillies' offense is back at full strength a day after beating the Marlins 9-1.
"Everybody thinks we're supposed to be scoring 20 runs a game," Howard said. "Sorry to inform you, it doesn't work like that."
Phillies left-hander Cole Hamels brushed off reporters a day after he left his start with tightness in the middle of his back. "I'm not injured. I'll talk to you guys in five days," he said. ... The Marlins optioned infielder Ozzie Martinez to Triple-A New Orleans and purchased Villanueva's contract. To make room for Villanueva, the Marlins transferred right-hander John Johnson to the 60-day disabled list. ... The Phillies have won four straight games in June for the first time since 2005. ... Marlins right-hander Edward Mujica left in the seventh with a sprained right wrist and is day to day.