Matsuzaka (5-2) gave up four hits — all singles — and was never threatened by Cleveland's punchless lineup. The right-hander continued a remarkable run by Boston's starters on the road. In the club's last nine games outside Fenway Park, the Red Sox rotation is 8-0 with a 0.70 ERA.
It was the 150th career win for Dice-K, who won 108 games in Japan before signing with the Red Sox in 2006.
He walked two, struck out five and allowed only two runners to reach second before he was replaced to start the ninth by reliever Daniel Bard, who gave up a leadoff homer to Austin Kearns.
Marco Scutaro hit three doubles and scored twice as the Red Sox improved to 9-2 on the road since May 18.
Boston made the most of its five hits off Fausto Carmona (4-5) in six innings.
The opener of the four-game series was a homecoming for Red Sox catcher Victor Martinez. The three-time All-Star was traded by the Indians last season before the July 31 deadline. Martinez was wildly popular during his eight seasons with Cleveland. He received a nice ovation before each at-bat and finished 2-for-4 with an RBI.
Carmona, whose record doesn't reflect how well he has pitched in a personal bounce-back season, only trailed 2-0 entering the seventh. But Scutaro led off with a double and eventually scored on Martinez's fly to deep left off Hector Ambriz, giving Boston a three-run cushion.
The Red Sox went up 4-0 in the eighth when Adrian Beltre doubled, went to third on a wild pitch and scored on Bill Hall's single.
Boston pounced on a fielding error by Carmona to open the third to take a 2-0 lead.
Josh Reddick dropped a leadoff bunt down the first-base line that Carmona bobbled after scooping and threw too late to first. Reddick stole second, moved to third on a forceout and scored when the Indians couldn't turn a double play to get the less-than-speedy David Ortiz.
Kevin Youkilis hit a sacrifice fly in the first to bring in Boston's first run.
Before the game, the Red Sox placed closer Jonathan Papelbon on the bereavement list. … Squeezed out of at-bats, Indians OF/1B Matt LaPorta was optioned to Triple-A Columbus. Manager Manny Acta said LaPorta, acquired in the 2008 deal from Milwaukee for CC Sabathia, will benefit more by playing every day in the minors than sitting and getting occasional time in Cleveland. Acta said the club sees LaPorta as a future first baseman. … Tito Francona, the father of Red Sox manager Terry Francona, visited his son before the game. The elder Francona drove over from his home in Western Pennsylvania. … The Indians selected LHP Drew Pomeranz with the No. 5 overall pick in the baseball draft. It was Cleveland's highest selection since 1992. Pomeranz went 9-2 this season for Mississippi.