Returning to Fenway Park as a manager for the first time since leaving the club he guided to two World Series titles at the end of the 2011 season, Francona saw his Indians punish Boston starter Ryan Dempster and the Red Sox bullpen, scoring in five of the first six innings.
Mark Reynolds and Drew Stubbs each drove in three on a trio of hits, while David Ortiz provided the only bright spot for the home fans with a three-run homer.
Mike Trout scored twice and hit one of four Los Angeles Angels home runs as they stretched their winning run to five by beating the Kansas City Royals 5-4.
Albert Pujols and Chris Iannetta also added solo shots, while Mark Trumbo crushed a two-run bomb in the eighth.
Edwin Encarnacion launched a grand slam to help the Toronto Blue Jays beat the Baltimore Orioles 12-6.
JP Arencibia also homered and drove in four for the Jays, while Chris Davis, with his Major League-leading 15th home run of the year, was one of three Baltimore players to go yard.
Miguel Cabrera hit his 14th homer of the season in the Detroit Tigers' 7-6 victory over the Minnesota Twins, while the Pittsburgh Pirates were 4-2 winners over the Chicago Cubs.