Manager Ned Yost overhauled his batting order and got immediate results. The Royals scored seven runs for the first time since Aug. 19, a span of 22 games.
Infante, who usually bats second, was dropped to seventh and responded with three singles, including an eighth inning single that scored Lorenzo Cain. He also drove in a run in the third with a fielder's choice.
Guthrie (11-11), who was roughed up for eight runs on 10 hits in 2 2-3 innings in a loss Monday at Detroit, allowed three hits and one unearned run in eight innings.
After David Ortiz's single in the third, Guthrie did not allow a base runner.
Rookie left-hander Brandon Finnegan, the Royals' top pick in this June's draft, replaced Guthrie and allowed one hit in the ninth.
Red Sox: INF Brock Holt remains sidelined with a concussion and there is no timetable for his return. He is still having vison problems.
Royals: LHP Danny Duffy, who skipped a start Thursday with a sore shoulder, is scheduled for a mound session Sunday. He is optimistic he will make his start Tuesday against Chicago. . DH Josh Willingham remains out with a groin injury.
Red Sox: RHP Joe Kelly will make his eighth start since being acquired in a July 31 trade with St. Louis. He last faced the Royals on June 22, 2012.
Royals: LHP Jason Vargas will start the series finale. He is 6-4 with a 3.98 ERA at home this season.