Cedric Mullins and Austin Hays hit back-to-back home runs to help the Orioles end their seven-game losing streak at Oakland.
Means beat the A's for the second time in six days.
''I just thought he located extremely well,'' Baltimore manager Brandon Hyde said. ''The pitch mix was there, adding and subtracting, pitching to both sides of the plate, pitching unpredictable. Facing the same team twice in week is not easy to do. That's a tough lineup to face once and he does it twice in a week and was outstanding.''
Sean Murphy and Mitch Moreland homered for the A's. Fiers lost in his season debut as Oakland fell to 2-4 since winning 13 straight.
Means (3-0) allowed one run and three hits over seven innings in another dominant outing by the Baltimore lefty. He gave up Murphy's leadoff home run in the second, walked Matt Chapman and then retired 18 of the next 20.
Means exited with a 1.70 ERA this season. He has permitted only three earned runs in four road starts this season, a span of 25 2/3 innings.
''I'm pretty comfortable with my mentality. Last year I would get really frustrated when things weren't going well,'' Means said. ''I've done a good job of staying within myself and letting the game come to me and just not making any moment too big, even with guys on base.''
Paul Fry retired two batters and Travis Lankins got Jed Lowrie to fly out with runners on the corners to end the eighth.
Cesar Valdez allowed two hits to open the ninth before retiring the next three batters for his sixth save. He got Elvis Andrus to fly out with the tying run on third.
The A's nearly tied it two batters earlier when Mitch Moreland hit a sharp liner to third baseman Rio Ruiz.
''Obviously we had an opportunity in the ninth and couldn't come through,'' A's manager Bob Melvin said. ''Moreland's ball was smoked. A few feet to the left and it's a whole different story.''
Fiers (0-1), who had been on the injured list with a hip problem, looked rusty in his first outing of the year. A 15-game winner for Oakland in 2019 who was initially tabbed to pitch out of the bullpen this season, he allowed three runs and six hits in six innings.
Fiers struck out three, walked three and pitched with runners on base in each inning except the first.
''I felt like I was right on track,'' Fiers said. ''Felt like I made really good pitches. They scrapped a couple runs against me and we couldn't get it back.''
Mullins, who had an RBI groundout in the fifth, hit his fourth homer of the season with two outs in the third. Hays followed with his third this year.
Orioles: 3B Maikel Franco (sore lower back) was held out of the starting lineup for this first time this season. . SS Freddy Galvis took full batting practice, did some defensive work and ran before the game as he works his way back from a left adductor injury. Hyde said Galvis could be back in Baltimore's lineup ''potentially within the next couple days.''
Athletics: 1B Matt Olson has improved after being hit near the eye by a ball that ricocheted off a screen during batting practice Thursday, when he was a late scratch because of the injury. His eye was ''a little bit open'' Friday but he hadn't recovered enough to play, though the slugger has passed tests for a possible concussion. ''Pretty scary situation, so we'll be careful with it,'' Melvin said. ... OF Chad Pinder, sidelined by a sprained left knee, is continuing his baseball activities and could begin a rehab assignment around May 10 with some simulated game work as soon as early next week.
Athletics LHP Jesus Luzardo (1-2, 5.40 ERA) faces the Orioles for the second time in seven days on Saturday. Luzardo allowed three runs in 6 2/3 innings on April 18 in his first career appearance against Baltimore. RHP Matt Harvey (2-1, 4.26 ERA) pitches for the Orioles and has not allowed a home run in two consecutive starts for first time since 2018.
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