Buchholz faced nine batters and got five outs on grounders. He walked one and struck out one.
Jackie Bradley Jr., trying to win a job in center field, gave the Red Sox a 2-0 lead in the second by grounding a two-run single into right field.
In the third, Carp hit his second home run of the spring onto the boardwalk in right-center.
Pirates right-hander Charlie Morton worked the first three innings and allowed three runs (one earned) on five hits.
Pittsburgh was hitless until the sixth, when Gregory Polanco led off with an infield single.
Red Sox: Buchholz breezed through the first two innings on 17 pitches. The only ball hit out of the infield during that stretch was Jaff Decker's blooper, which was caught by left fielder Alex Hassan.
Pirates: Morton struggled in his third outing this spring. He let six of his 16 batters reach base.
"It was just bad," Morton said. "I was falling behind hitters. When I was ahead of hitters, everything turned out OK. The problem was I didn't get ahead of many."
Red Sox: Right-hander Jake Peavy, who has a gash on his non-pitching hand, is expected to start Thursday. Peavy threw a simulated game Saturday. ... Outfielder Shane Victorino (lower back tightness) will play Monday or Tuesday. "It won't be both," manager John Farrell said. The Red Sox are off Wednesday.
Pirates: Travis Ishikawa played in his first spring game after sitting out with a tight right hamstring. As the designated hitter, he went 0 for 2 with a strikeout. Ishikawa came to camp as a fringe candidate for a backup spot at first base and right field, but likely is ticketed for Triple-A Indianapolis.
Red Sox: Bradley is getting pressure from Grady Sizemore for a spot on the opening-day roster. Sizemore did not travel to Bradenton, but is expected to be in the lineup Monday and Tuesday. If Sizemore shows he's healthy and wins the spot, Bradley would likely begin the season at Triple-A Pawtucket. Bradley went 1 for 4 with two RBIs on Sunday. He is 4 for 21 with five strikeouts this spring.
Amid reports that the Red Sox are unhappy with the play of third baseman Will Middlebrooks, Farrell declined to discuss whether the team would reconsider re-signing infielder Stephen Drew. "I really don't have anything to say about Drew," Farrell said. "He's a free agent and that's where it stands."
Pirates: Chris Dickerson, who hit .238 in 56 games last season with Baltimore, is trying to make the roster as a fifth outfielder. Dickerson has a .262 career batting average, but his forte is defense. "He's quick, he's got instincts and savvy," outfield coach Rick Sofield said. "Chris was covering ground (Saturday) as well as any center fielder I've been around. He's the real deal on defense."
CALL TO THE `PEN
Red Sox: Francisco Cordero has pitched well so far, but still faces an uphill battle to crack the opening-day bullpen. The 38-year-old right-hander last pitched in the majors in 2012 with Toronto and Houston. Cordero tossed one scoreless inning Sunday and has allowed three hits in four scoreless appearances.
"He's not pitching like a guy who's been out for a year," Farrell said. "He's thrown a lot of strikes. He's made the necessary adjustments. As a pitcher gets deeper into his career, he has to pitch a little bit more and use an assortment of pitches, rather than just relying on velocity. He's showing that in spring training."
Pirates: The back-end combo of setup man Mark Melancon and closer Jason Grilli dominated in what was the second spring outing for each pitcher. Grilli got two strikeouts and a foul popup. Melancon struck out Hassan and David Ross and got Carp on a grounder.