They leave after losing three out of four and watching their AL wild-card hopes fall apart.
''The guys are still fighting. We're looking to make some noise,'' right-hander Mike Bauman said after the Red Sox won 5-3 to send the Orioles to their fifth loss in six games. ''Things didn't necessarily go our way, but there's a lot of baseball left and we're looking to get back on our feet this next series in New York.''
J.D. Martinez hit a two-run homer to break an eighth-inning tie, Zack Kelly earned his first career victory and Boston beat Baltimore for the third straight game. The Orioles were 3 1/2 games out of the final AL wild-card spot after winning the series opener but face the first-place Yankees this weekend needing to overcome a five-game deficit to Tampa Bay with just six games to play.
''We've been in close games and just haven't really finished,'' Kyle Stowers said.
Baltimore led 2-0 before falling behind, then tied it at 3 on Stowers' seventh-inning homer. But Dillon Tate (4-4) walked the leadoff batter in the eighth and one out later Martinez sent a ball over the Green Monster and onto Lansdowne Street.
Toronto clinched a playoff berth because of Baltimore's loss. Seattle and Tampa Bay are in position for the other two AL wild-card spots.
Martinez and rookie Triston Casas each had two hits for Boston, which won its third straight game and took the season series from Baltimore (10-9) for the fifth straight year.
Zack Kelly (1-0) allowed one hit and struck out one in one shutout inning. Kaleb Ort pitched the ninth for his first career save.
Stowers also singled and scored in the third to start a two-run rally. Gunnar Henderson and Cedric Mullins also had two hits apiece for the Orioles.
After trailing 2-0 early and tying the score with two runs in the fourth, the Red Sox took the lead in the sixth inning on Christian Arroyo's RBI groundout. But Stowers tied it with a solo homer.
The Red Sox ballpark in Fort Myers, Florida, sustained wind damage from Hurricane Ian but the extent of the damage was not yet known. The team has trained in the city in southwestern Florida since 1993 and opened JetBlue Park in 2012.
''The reports coming out of Lee County in the wake of Hurricane Ian are devastating and our hearts go out to those impacted,'' the team said in a statement. ''The Red Sox organization will work with our partners in Lee County to provide resources and support for recovery efforts.''
Red Sox starter Nathan Eovaldi pitched 4 2/3 innings, making his first appearance since going on the injured list on Aug. 23 with a sore right shoulder. He allowed two runs - one earned - on five hits while striking out three.
Baltimore's Mike Bauman gave up two runs in four innings, allowing six hits and striking out two.
Orioles catcher Adley Rutschman doubled in the first inning - his 33rd of the season. That broke Cal Ripken Jr.'s franchise record for a rookie set in 1982.
''Obviously Cal Ripken - he is the Orioles,'' Rutschman said. ''It's definitely a cool thing.''
The 33 doubles is also the most for an Orioles catcher since Javy Lopez had 33 in 2004.
Orioles: Open a weekend series in New York against the Yankees. Baltimore RHP Jordan Lyles (11-11) will face RHP Domingo German (2-3).
Red Sox: Move to Toronto for a three-game series. Boston RHP Nick Pivetta (10-11) will start the opener. The Blue Jays have not announced a starter.
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