MIAMI -- The booming hip-hop on the stereo in the Cleveland Indians' postgame clubhouse was quickly dialed down to low volume, and the celebration following their 15th shutout victory of the season was muted.
The team had a plane to catch, and a big series to play beginning Monday.
The Indians begin a four-game series at home Monday against AL Central leader Detroit. With the win against Miami, Cleveland remained three games behind the Tigers.
"I'd rather be 10 up," manager Terry Francona said. "But this makes this really exciting. We get to play the best team in our division and see how we can do."
The Indians took two of three games from Miami despite scoring a total of only six runs.
Kazmir (7-4) won his fourth decision in a row by limiting the Marlins to two hits in six innings. Bryan Shaw, Joe Smith and Chris Perez pitched one inning each for the Indians, who lead the majors in shutouts.
"It means we're getting some solid pitching," Francona said. "And if you're going to go somewhere in this game, you need pitching."
Shaw gave up two singles in the seventh but also struck out the side. Perez earned his 17th save in 19 chances by pitching a perfect ninth with the help of a diving catch by center fielder Michael Bourn.
Kazmir was pleased with his outing, the 200th of his career, but the left-hander's grin grew widest as he discussed his fifth-inning single, his first hit since 2007.
"That was great," he said. "A lot of trash-talking has been going on the past couple of days -- actually pretty much the whole year. So it was good to get that."
Manager Jack McKeon and 13 players from the Marlins' 2003 World Series championship team were on hand to celebrate their 10-year anniversary, but their success wasn't contagious.
Miami, which ranks last in the majors in runs and batting, was shut out for the 13th time. With runners in scoring position, the Marlins went 0-for-4 with three strikeouts.
"We're not getting a ton of hits, and in a game like this that hurts you," manager Mike Redmond said.
Slumping slugger Giancarlo Stanton went 0-for-4 with two strikeouts and finished the series 1-for-11 with five strikeouts, dropping his average to .245.
"It's something you just go through, and it always works itself out eventually," he said.
Nathan Eovaldi (2-2) allowed only one run in seven innings and hit 100 mph on the radar gun. The Marlins haven't scored when Eovaldi's on the mound over his past four starts.
"That kid has a tremendous arm," Francona said. "When you got the ball down there wasn't much you could do with it."
Marlins pitchers have gone 12 consecutive games without allowing a home run, the longest such streak in the majors since the 1998 Braves had streaks of 14 and 12 games. The streak nearly ended when Mark Reynolds doubled off the left-field fence in the second inning.
That put runners at second and third, and Chisenhall stumbled and fell halfway down the first-base line as he ran out a grounder that went foul. He sheepishly rose and returned to the plate, then hit the next pitch for an RBI single and a 1-0 lead.
Brantley ended an 0-for-14 slump when he hit a two-out, 3-2 pitch for an RBI single in the eighth. He's batting .346 this year with runners in scoring position.
"It was a battle," Brantley said. "I fouled off a couple of hard sliders. It was nice to get a little breathing room."
With the victory, Cleveland won a road series for the first time since June.
Bring on the Tigers.
"We've got to defend our home territory," Brantley said. "We'll see where we stand."
The Marlins fell to 4-10 in interleague play. ... The Indians didn't attempt a steal against C Jeff Mathis after going 6 for 6 Saturday, when Rob Brantly was behind the plate. ... Miami's Ed Lucas was awarded a ground-rule double in the first inning when the ball became wedged in the base of the left-field fence under an advertising sign. He was stranded there. ... RHP Corey Kluber (7-5) is scheduled to pitch Monday for the Indians against the Tigers' Anibal Sanchez (9-7).