Doubront's 31-pitch first included three walks, a wild pitch and a hit batter, as well as two runs, but he recovered and allowed just one more run as he registered a quality start, striking out eight and scattering four hits in 6 2/3 innings.
David Ortiz led the Boston offence, driving in three runs on two hits and improving his average to .519 as the Red Sox took their record to a league-best 16-7.
Back-to-back homers from Nick Markakis and Adam Jones helped the Baltimore Orioles to a 7-3 win over the Oakland Athletics.
Nate McLouth also went yard while Josh Tillman got his first win of the season on six innings of two-run ball.
Josh Willingham homered to lift the Minnesota Twins to a 7-2 victory over the Texas Rangers.
Pedro Hernandez hurled five shutout innings for his first win in the majors.
Travis Hafner had a home run and four RBI as the New York Yankees beat the Toronto Blue Jays 5-4.
Matt Moore racked up his fifth win of the season, striking out nine and allowing one run in six innings to lift the Tampa Bay Rays past the Chicago White Sox 10-4.
Omar Infante and Jhonny Peralta had a two-run homer apiece to lift the Detroit Tigers to a 7-4 win over the Atlanta Braves.
And there were two-run bombs for Carlos Gomez and Martin Maldonado as the Milwaukee Brewers overcame the Los Angeles Dodgers 6-4.
Yonder Alonso scored the winning run in the 12th as the San Diego Padres rallied from 5-0 down to beat the San Francisco Giants 8-7.
Cody Ross drove in AJ Pollock with a sacrifice fly to give the Arizona Diamondbacks a 3-2 10-inning win over the Colorado Rockies.
Bryce Harper hit his ninth home run of the season, a two-run shot in the fourth, to help the Washington Nationals overcome the Cincinnati Reds 6-3.
Ervin Santana produced seven scoreless innings to help the Kansas City Royals edge out the Cleveland Indians 3-1 and the Seattle Mariners overcame the Los Angeles Angels by the same scoreline.
The Philadelphia Phillies beat the New York Mets 9-4, the Pittsburgh Pirates were 5-3 winners over the St Louis Cardinals and the Chicago Cubs edged out the Miami Marlins 3-2.