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.
"Breathing room, we haven't had a whole bunch of that recently," Guthrie said. "I don't know if you ever get too comfortable [whether] you have two or three runs. But once you get seven, you're a little more comfortable."
The Royals remain a half-game behind Detroit in the AL Central standings. After losing four of their previous five games, it was important for the Royals to keep pace with the Tigers.
"I think we've approached all the games the same," Guthrie said. "That's the easiest way to do it. I think if you try to approach every game differently -- like yesterday was less important, and today's and tomorrow's are subtly important, but Monday's game is way more important. I think it is difficult to prepare like that."
Nori Aoki, batting second for the first time this season, and Alex Gordon, who snapped an 0-for-22 skid, each had two hits, scored a run and drove in a run. Alcides Escobar also had two hits, including a double to start the game.
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.
"It was huge," Cain said of scoring two in the first. "We've been struggling to score runs, but to get two early was outstanding for us. We definitely need to score runs. We did a great job of that tonight, but we've got to keep doing it."
Guthrie (11-11), who was roughed up for eight runs on 10 hits in 2⅔ innings in a loss Monday at Detroit, allowed three hits and one unearned run in eight innings.
"He was in control," Yost said. "He just pitched a great game. He was on tonight."
After David Ortiz's single in the third, Guthrie did not allow a baserunner.
"He was very good," Red Sox manager John Farrell said. "We didn't really manufacture anything against him."
Fifteen of Guthrie's 24 outs were fly outs, with center fielder Jarrod Dyson tracking down nine.
"He had the fly ball going for him," Red Sox center fielder Jackie Bradley Jr. said. "He was efficient with his pitches."
"Every time he walks to the mound it's a good test, regardless of the number of innings pitched in a given year," Farrell said. "We are limiting his innings pitched, but we don't want to shut him down."
Cain swiped his 25th base, joining Dyson and Escobar in the 25-steal club. The last time the Royals had three players steal 25 bases in a season was 1983 -- Willie Wilson, John Washington and U.L. Washington.
Red Sox: INF Brock Holt remains sidelined with a concussion and there is no timetable for his return. He is still having vision 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.