Mike Napoli and Daniel Nava each drove in a pair of runs as Boston doubled up Cleveland, 6-3, in the second edition of a three-game series.
Mike Carp finished 3-for-3 with a pair of doubles and an RBI triple for the Red Sox, who have taken the first two in the set and five straight overall.
"I don't want to downplay the events that we just left in Boston, but I think what we've quickly come to see is a group that likes to be around one another," Farrell said of his remade roster. "'Those are encouraging signs."
Boston starter Alfredo Aceves (1-0) pitched into the sixth inning, snagging the decision after allowing seven hits and three runs. Andrew Bailey fanned two in a scoreless ninth to earn his first save.
Nick Swisher hit a two-run homer and Jason Giambi added a solo shot for the Indians, losers in three straight.
Justin Masterson (3-1) was tagged for 11 hits and four runs in defeat despite five strikeouts over five innings.
"It wasn't as fun as the last three I pitched, but over a season when you have 30-plus starts you're going to have some like this," Masterson, an ex-Red Sox pitcher, said. "I kept it close as much as I could."
Picking up where they left off on Tuesday, the Sox exploded for three runs in the first, thanks to a two-run single from Napoli followed by an RBI hit by Nava.
Boston failed to increase its lead with the bases loaded in the second, but picked up one more in the fifth on an RBI triple from Carp and stretched its advantage to 5-0 in the sixth on a Nava base hit which plated Shane Victorino.
Carlos Santana started the home sixth with a walk, then Swisher deposited an Aceves pitch over the wall in center for a 5-2 game. Giambi followed with his first of the year, and Mark Reynolds doubled before Aceves was lifted for Junichi Tazawa, who prevented further damage.
Tazawa turned in a scoreless seventh, and Jacoby Ellsbury led off Boston's half of the eighth with a single before advancing to second on a wild pitch and scoring when Tribe reliever Joe Smith threw wild to first on a Victorino sacrifice bunt.
"The two innings by 'Taz' were probably the difference in the ballgame," said Farrell. "He had some real good stuff, threw a lot of strikes."
Koji Uehara extended his scoreless string with an uneventful eighth, and Bailey finished up by retiring the side in order.
Ellsbury and Victorino also collected three hits, part of Boston's 15-hit barrage ... Uehara has gone 18.0 consecutive scoreless frames dating back to Sept. 1, 2012, setting a personal career-long streak in the majors ... At 42 years of age, Giambi became the third-oldest player to hit a home run in Indians history, after Sam Rice (44) in 1934 and Dave Winfield (43) in 1995 ...As they did for Tuesday's opener, the Red Sox hung a road jersey with "617," Boston's core area code, to honor those hurt and killed in the Marathon bombings on Monday.