Jon Lester dazzled for a fourth straight start, firing seven strong innings for the win.
Timely hitting was present throughout the night, and from various spots in the lineup.
Aggressive and heads-up baserunning led directly to at least a couple of runs.
Boston heads back to Fenway with an 11-4 record -- the best start the club has had since 2006.
"We're trying to play the game right, take the extra base and do the little things to help us win the ballgame," said Dustin Pedroia. "We've been doing that lately, we've got to continue to do that."
The Sox will get David Ortiz back on Friday night against the Royals, as he makes his season debut after an eight-month battle back from problems with his right Achilles heel.
And this will also be the first game at Fenway Park since Monday's tragedy at the Boston Marathon, when multiple bombs killed three people and injured 176 others.
The three who were killed were on the mind of Lester, who later tweeted: "Took Martin Richard, Krystle Campbell, Lu Lingzi and all those who were injured Monday out there on the mound with me tonight."
He said he was looking forward to returning to Boston.
"It's going to be great, go back there and get in front of those fans," said Lester. "It goes back to the same things we talked about. Maybe for a couple of hours, they can get back to just being Boston, watching a baseball game and having a good time and not thinking about all the other things. Hopefully we're able to do that and at the same time play good baseball on top of that."
The Sox have been doing a lot of that of late, thanks to performances like this one from Lester. The lefty, who pitched against former manager Terry Francona for the first time, is 3-0 with a 1.73 ERA.
"Lester has a lot of ways to attack hitters," said Francona. "Whether it's depth on his two-seamer or life on the fastball, and then he's got that cutter. And he threw an occasional breaking ball. He has a lot of ways of opening up the plate."
For Francona, this was not the reunion matchup he was looking for. The Indians come to Fenway from May 23-26.
"I didn't enjoy the series much," Francona said. "But I'll never get tired of seeing people I care about."
The Red Sox jumped out in front yet again, as Mike Napoli led off the second with a triple to right and Daniel Nava got him home with an RBI single. It was the seventh career triple for Napoli.
"I never think triple -- ever," said Napoli.
The Indians got a run right back in the bottom of the second. Mark Reynolds started it with a grounder down the third-base line that took a bad hop on Pedro Ciriaco for a ground-rule double. Ryan Raburn drilled a fly ball to deep right and Reynolds moved to third. Mike Aviles tied it up with a fielder's choice grounder.
But when Jarrod Saltalamacchia put a charge into a 3-2 fastball from Indians starter Zach McAllister with two outs in the fourth, the game was no longer tied. Saltalamacchia capped his seven-pitch at-bat by walloping the ball over the wall in right for a solo shot, his third homer of the season.
"Well, when he gets fastballs on the plate he can do a lot of damage and he took some borderline curveballs that from the side view were good pitchers' pitches," Farrell said. "He was able to get back in the count and when he gets a fastball around the plate, we know what he's very well capable of."
This was a night when the Boston bats continued to chip away. In the fifth, Jacoby Ellsbury doubled and Shane Victorino singled, setting up Pedroia, who executed a hit-and-run perfectly for an RBI single to right. A fielder's choice RBI by Drew Stubbs in the bottom of the fifth made it a 3-2 game.
Boston created some breathing room in the seventh. Ellsbury led off with a single. Victorino caught a break, as second baseman Cord Phelps bobbled his grounder for an error. When Pedroia belted one to deep right, narrowly missing his first homer of the season, Ellsbury tagged and moved to third. That gave Napoli -- who has been an RBI machine for Boston -- the chance to drive in Ellsbury with an RBI single to right.
Not only were the Red Sox scoring, but they were hustling. Nava delivered a sac fly to center, and when the throw came home, Napoli tagged and made it to second.
"We're going to be aggressive on the bases," Napoli said. "We're not going to be crazy and try to run into outs, but in that situation, Stubbs has a really good arm, especially when he's coming forward and is under the ball. That run on third was a key run, so I was mainly try to make him cut it so we'd get that three-run lead. I thought he was going to let it go and I'd be on second, but fortunately he bobbled it at second and we got another big run out of it."
That paid dividends when pinch-hitter Mike Carp came off the bench and banged an RBI single to right, scoring Napoli.
"It's fun to watch," Lester said. "Guys take the extra base. They're aggressive, but also under control. The at-bats guys guys are putting together just fouling off pitches and grinding them out, it's been fun. And then seeing our bullpen come in and doing what they've been doing lately. You can't put your finger on one thing. Everybody's doing what they need to do and we're playing good baseball right now."