Matsuzaka (8-3) allowed Shin-Soo Choo's 14th homer of the season in the first but gave up just four more hits and never faced more than four batters in any inning. He is 5-1 in his last 10 starts and has allowed three earned runs or less in 10 of his last 12 outings.
Beltre connected for his 20th homer in the fourth inning after Josh Tomlin (1-1) retired Boston's first 10 batters. Beltre took over the team's RBI lead with 75.
Jonathan Papelbon got his 26th save in 31 opportunities when he struck out Trevor Crowe with the bases loaded for the final out.
Marco Scutaro singled with one out in the fourth for Boston. After David Ortiz flied out, Victor Martinez and J.D. Drew walked before Beltre hit a 1-0 pitch for his eighth grand slam and first since Sept. 21, 2006. It extended his hitting streak to 11 games.
The homer capped Beltre's big series against Cleveland. He started it by driving in all of Boston's runs in a 6-5 loss Monday night and finished 6-for-15 with four runs scored, three homers and nine RBIs.
Drew drove in Boston's last two runs in the eighth with a single.
Cleveland scored on Luis Valbuena's ninth-inning single off Hideki Okajima before Papelbon took over.
The Indians lost a chance for their first series win at Fenway Park since 2005, while the victory sent the Red Sox off a tough 10-game road trip on a high note. They open a four-game series against the New York Yankees on Friday night, then play three games each at Toronto and Texas.
Boston is trying to stay in contention for a postseason berth despite a rash of injuries. The latest to be sidelined is first baseman Kevin Youkilis, who is scheduled to undergo season-ending surgery on his right thumb on Friday in Cleveland. Second baseman Dustin Pedroia missed his 34th game Thursday with a fractured left foot and still can't run without pain.
Going into their game on July 4, the Red Sox were a half-game out of first place in the AL East. Now they trail the first-place Yankees by six games for the division lead and Tampa Bay by 5 1/2 in the wild-card race.
Matsuzaka was coming off one of his poorer outings of his strong season when he left last Saturday's game in the seventh with Detroit leading 4-0. But Boston rallied for a 5-4 win.
Against Cleveland, he struck out six, walked two and allowed five hits. After Jayson Nix led off the seventh with a single, Matsuzaka retired the last six batters he faced.
Tomlin started the game the way he pitched in his first two major league starts. He allowed one earned run in seven-plus innings and got the win in his debut, a 3-1 win over the Yankees, then got a no-decision in a 2-1 win at Toronto in which he gave up one earned run in 5 1-3 innings.
He settled down after Beltre's homer, giving up two more hits before leaving after the seventh.
Notes
Ortiz's 13-game hitting streak ended when he went 0-for-3. … Choo's homer extended Cleveland's streak to 58 games with an extra-base hit, the longest current stretch in the majors. … Before the game, the Indians acquired C Juan Apodaca and IF Argenis Reyes, who have been at Boston's Triple-A team in Pawtucket, for cash.