Doubront went 6 1/3 innings, the longest outing of his career, to save an overworked Red Sox bullpen in an 11-5 victory over the Kansas City Royals. He yielded five runs, four earned, on seven hits and three walks to pick up the victory.
Boston had lost 9-6 to Baltimore in a 17-inning game Sunday.
"Felix was excellent," Red Sox manager Bobby Valentine said. "He was exactly what we needed. Three of the hits off him were a bunt, an infield single and a broken-bat single. He was efficient. He was terrific."
After Doubront (2-1) walked Alex Gordon with the bases loaded in the seventh to cut Boston's lead to 7-5, Vicente Padilla replaced Doubront and coaxed Billy Butler to ground into an inning-ending double play. Padilla held the Royals scoreless for 2 2/3 innings to pick up his first save.
Middlebrooks, who hit a grand slam Sunday, homered with David Ortiz and Adrian Gonzalez aboard in the Red Sox four-run first. Middlebrooks also hit a two-run homer off the left field foul pole in the four-run eighth, giving him nine RBI in two games.
"It's not just about that," Middlebrooks said. "It was a team win. Doubront pitched his butt off, and we got good pitching from the bullpen again."
Royals left-hander Jonathan Sanchez (1-2) said he thought he threw a decent pitch to Middlebrooks in the first inning, but the rookie was ready for it.
"I felt he would try to go away against me," Middlebrooks said. "I watched a lot of video on him and felt that he was going to go away. I wanted to approach it that way."
Ortiz, who had three hits and was twice walked intentionally, and Dustin Pedroia also homered for the Red Sox, who snapped a five-game losing streak. Pedroia and Ortiz each scored three runs.
The Royals dropped to 0-5 when the opponent starts a left-hander and to 2-13 at Kauffman Stadium.
Ortiz homered to lead off the Boston third. After Kelly Shoppach tripled -- his first career triple in 472 big league games -- off the left field bullpen fence to open the fourth, Royals manager Ned Yost pulled Sanchez, who threw only 35 strikes in 73 pitches. Sanchez was charged with six runs on six hits and three walks while retiring only nine of the 18 batters he faced.
"I didn't think I got hit pretty well," Sanchez said. "I made a good pitch to the guy who hit the three-run home run. When he hit it, he didn't know where it was. He got lucky. After that, the home run Ortiz hit, and that was it. I pretty much made good pitches. I gave up a couple of hits."
Yost did not echo Sanchez's sentiments on how he pitched.
"Starting pitching sets the tone," Yost said. "Sanchez once again really struggled to command his fastball. His secondary stuff was decent enough. He got his pitch count way up early. They put a four-spot on him in the first inning. It was just a struggle for him tonight to command the baseball.
"His last start against Detroit, he took a no-hitter into the fifth inning, commanded his fastball and going into the fifth inning had not thrown a walk. We were hoping that would duplicate tonight, but obviously it didn't."
Nate Adcock, who replaced Sanchez, gave up a two-run homer to Pedroia in the fourth, giving the Red Sox a 7-4 advantage.
"The game had a feel like if we could just hold them, we were going to climb back into it," Yost said. "The offense is starting to come around. We just need to get that starting pitching settled in and we're going to be OK."