Pittsburgh (9-14) has won just twice in its last eight games, though both victories have come at Boston's expense. The Red Sox are now 12-12-1 in Grapefruit League play.
Boston's Josh Beckett shouldered the loss even though the right-hander allowed just one earned run in 4 2/3 innings. An error by first baseman Nate Spears in the fourth allowed Pittsburgh to score four unearned runs off Beckett, who also gave up seven hits and one walk.
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Spears' two-base throwing error allowed Neil Walker to reach leading off the frame. After Andrew McCutchen drew a walk, Overbay drove both home with a double to left-center. Overbay, who had one other hit off Beckett on Saturday, pushed his hitting streak to 10 games and is 15-for-37 (.405) this spring.
Matt Diaz and Dusty Brown extended the inning with singles, which brought Correia to the plate. The Pirates starter, who had singled his first time up, brought in two with his second hit of the afternoon.
The Red Sox cut into that 5-0 lead the following inning by scoring three times off Correia. After Darnell McDonald walked, Boston strung together singles from Daniel Nava, Spears and Marco Scutaro to score two. An error by Walker allowed one more run to score before Correia worked out of trouble to end the threat.
Correia, who struck out four and allowed seven hits in five innings, was replaced by Joel Hanrahan in the sixth. Hanrahan gave up one hit and struck out two in the scoreless relief appearance.
"The first inning, I was kind of getting my feel," Correia said. "I felt pretty good after that. Then they barreled a couple of balls in the fifth. But all in all, I felt strong through 80 pitches. At this point, I feel like I could make a regular-season start."
Both Scutaro and Dustin Pedroia had multi-hit games for Boston, which has lost its last three games. Pedroia is 12-for-36 (.333) this spring. The Red Sox scored again in the seventh on a wild pitch from Pirates reliever Justin Thomas, who is fighting for a bullpen spot.
Dan Wheeler made a scoreless appearance out of the 'pen for the Red Sox, while Alfredo Aceves allowed two runs in three innings.
Up next for the Pirates: The Pirates will meet the Astros for the first time this spring in the club's only trip to Kissimmee, Fla., on Sunday. Charlie Morton gets the start for Pittsburgh in the 1:05 p.m. ET contest. Morton, who will be opposed by Houston's Ryan Rowland-Smith, is scheduled to be followed by Evan Meek, Mike Crotta and Chris Leroux.
Up next for the Red Sox: Daisuke Matsuzaka starts for Boston at home in Fort Myers, Fla., against St. Louis at 1:05 p.m. ET on Sunday. Scott Atchison is to pitch, as are a trio of lefties: Andrew Miller, Rich Hill and Dennys Reyes. Kyle McClellan, who's competing for a rotation spot, starts for the Cardinals.
Jenifer Langosch is a reporter for MLB.com. Read her blog, By Gosh, It's Langosch, and follow her on Twitter @LangoschMLB. This story was not subject to the approval of Major League Baseball or its clubs.