Alonso, traded from Oakland on Aug. 6, hit a two-run homer in the fourth inning, his 23rd of the season. An All-Star this year with the A's, he added an RBI single during a three-run fifth and also singled in the seventh.
"I think he's been swinging the bat great the last three, four days," said Mariners manager Scott Servais, who was ejected in the ninth inning. "It's really been much better. He's been much more aggressive, it looks like the guy we saw early in the year when he was with Oakland."
Leonys Martin opened the sixth with his third home run to put Seattle up 7-4.
Seattle closer Edwin Diaz came on in the ninth and walked the first three hitters. Manny Machado followed with a sacrifice fly to make it 7-5, but Martin prevented an extra-base hit with a sensational diving catch in right field.
Diaz struck out Jonathan Schoop, but then hit both Trey Mancini and Mark Trumbo to force in another run. Rzepczynski relieved and fanned Davis on three pitches for his first save, and just the second in his career.
"I've come in with the bases loaded, two outs plenty of times, but never in the ninth with the game on the line," said Rzepczynski, whose only other save in 466 appearances was with Cleveland in 2014. "One other career save, and it was a four-out save, so it was a little different. But, I've come in plenty of times with the bases loaded, so I kind of just treated it like that."
The breaking balls weren't there since the beginning of the game," Jimenez said. "The first couple innings I was able to control the fastball down in the zone, but then the slider and the splitter were up."
The wild card-contending Mariners won their second in a row and capped a 2-5 homestand, their only games at Safeco Field in August. Seattle opened the month with eight games on the road, and now heads out on a four-city, 12-game trip.
"It's definitely nice," said Alonso, who entered hitting .192 in his first seven games with Seattle. "Obviously, I'm enjoying my time here and enjoying the opportunity for this whole team and what's at stake. We're excited and it was a good team. Definitely a good one, especially winning the series, so now we can enjoy our off day and get ready for a long road trip."
After Baltimore erased a 3-1 deficit with three runs in the fifth, the Mariners answered with three in the bottom half to go back in front 6-4. Jean Segura singled to open and Guillermo Heredia was hit by a pitch, setting up RBI singles by Robinson Cano, Alonso and Danny Valencia.
The Orioles bunched five consecutive one-out hits to go up 4-3 in the fifth. Joey Rickard and Caleb Joseph had consecutive singles. Rickard scored from third on a wild pitch and Craig Gentry followed with an RBI triple to left-center. Tim Beckham singled in Gentry.
"It's one of those games where you look back, there's seven or eight things during the course of the game that could have changed it," Orioles manager Buck Showalter said.
Beckham opened the game with his 17th home run, his second leadoff homer of the series. The Mariners tied it in the third on doubles by Mike Zunino and Heredia.
Servais was ejected in the ninth inning by first base umpire Stu Scheurwater. Servais thought Mancini swung through the third strike when he was hit by the pitch. "He swung," Servais said. "And, if he swings, whether it hits him or not, it is strike three and the game is over. That was my beef with it. I think it's pretty clear when you watch it on replay. Again, it's a judgment call by the umpire."
Orioles: CF Adam Jones didn't play, giving him a two-day breather because of Thursday's day off.
Mariners: 3B Kyle Seager missed his second straight game with what was described as a stomach virus. Valencia made his first start of the season at 3B. ... RHP James Paxton, on the 10-day DL (strained left pectoral muscle) continues to improve. "Paxton was seen by the doctor yesterday, moving along in the right direction. He'll start really picking up his activity now and trying to strengthen things," manager Scott Servais said.
Orioles: After this 10-game road trip, Baltimore is off Thursday and opens a three-game series at home against the Angels on Friday. The Orioles have not yet determined their starter for Friday.
Mariners: After a day off, RHP Erasmo Ramirez (4-4, 4.73) returns to Tampa Bay to open the three-game series on Friday. Ramirez, acquired from the Rays on July 28, makes his fourth start for the Mariners. He has allowed five homers in 14 1/3 innings with Seattle.
Andrew McCutchen and Evan Longoria open up about the upcoming season in their new home of San Francisco.
Rays pitching prospect Brent Honeywell left the mound during a live batting practice session with what the team diagnosed as a right forearm strain.
Houston Astros star shortstop Carlos Correa has always been a solid defender, but he is looking to take that part of his game to the next level.
For a second day in a row, the Red Sox said there would not be a news conference to introduce free-agent slugger J.D. Martinez because his physical had not been completed.
Surprised to be traded, Steven Souza Jr. heads to Arizona for what promises to be a key role on a Diamondbacks team that expects to be good.
Mariners catcher Mike Zunino enters his sixth season after setting several career highs at the plate in 2017, when he hit .251 with 25 home runs and 64 RBIs.