Mike Napoli's three-run double punctuated a seven-run second inning as Boston downed Cleveland, 7-2, in the opener of a three-game series.
Jacoby Ellsbury, Dustin Pedroia, David Ross and Pedro Ciriaco were credited with an RBI each for the Red Sox, who were coming off a weekend sweep of the Rays.
Felix Doubront (1-0) worked five innings for the win, allowing four hits and two runs, fanning seven and walking four.
"Given the events that have taken place...this was a good way to send some positive energy back towards Boston," Red Sox manager John Farrell said, referring to the tragedy during Monday's Boston Marathon.
Michael Brantley collected two hits and Mike Aviles knocked in a run for the Indians, who had won two of three in Chicago.
Ubaldo Jimenez (0-2) was lit up for two hits and seven runs, including five walks, while recording only five outs.
"Everything felt good coming out of my hand (early on), but then it just failed me fast," Jimenez said.
Tuesday's series opener was the first for Indians manager Terry Francona against the club which he guided for eight seasons (2004-11) and whom he helped win two World Series titles.
The Sox blew the game open in their second turn at the plate. A double from Napoli and walks to Will Middlebrooks and Jonny Gomes loaded the bases with one out, then Ross added a base on balls to force in a run, Ciriaco's fly plated another, then Ellsbury's hit made it 3-0.
Ellsbury swiped second ahead of a walk to Shane Victorino, and after Pedroia worked another walk which forced in another run, Cody Allen replaced Jimenez. Napoli capped the surge when he doubled home everyone on base.
Cleveland got a run back in the home half as Nick Swisher singled, moved to third on a Brantley base hit and scored on an Aviles fly to right.
The hosts' only other answer occurred in the home fifth. Ryan Raburn singled with one out, Drew Stubbs walked, then Asdrubal Cabrera singled to fill the sacks. Two batters later, a Ross passed ball plated Stubbs, and though Doubront dug himself in deeper by walking Swisher to re-load the bases, he ended his outing by inducing a pop out from Mark Reynolds.
Clayton Mortensen then turned in two scoreless frames, and Alex Wilson completed the job with two more unblemished innings.
Despite the win, Boston batters struck out 16 times against Cleveland pitching, while walking nine times and collecting just six hits ... Francona exited Boston with a regular-season record of 744-552 ... Prior to the game, the Sox placed relief pitcher Joel Hanrahan on the 15-day disabled list due to a strained right hamstring, retroactive to April 14 ... To fill the roster spot, the Red Sox recalled pitcher Steven Wright from Triple-A Pawtucket.