Shohei Ohtani hit his eighth home run for the Angels, who chased Seattle starter Chris Flexen after four innings.
Four Mariners relievers combined to hold Los Angeles to one run and two hits in five innings as Seattle earned its eighth come-from-behind win this year.
Drew Steckenrider (2-1) entered at the start of the fifth and retired six straight batters, striking out the side in the sixth. Both Mike Trout and Anthony Rendon had words for plate umpire Lance Barrett in the inning after called third strikes.
''He needed to pitch,'' Mariners manager Scott Servais said. ''He hadn't been out there in four days, so he was our freshest arm. It was the perfect spot to put him in and he really did quiet the game down.''
Steckenrider was especially pumped about the Trout strikeout.
''That was the first time I got to face him, so I wanted to go right after him and not hold anything back,'' the reliever said.
Casey Sadler and Anthony Misiewicz also contributed 1-2-3 frames as the bullpen improved to 9-4 in April with a 2.35 ERA.
Haniger hit his sixth career leadoff homer after two days off due to soreness.
Moore homered in the second to tie it at 2, drove in Ty France with a single in the third to make it 3-all and manufactured a run in the sixth to give Seattle a two-run lead. He drew a walk, advanced on Junior Guerra's wild pitch, stole third and scored on catcher Kurt Suzuki's errant pickoff throw.
''It's no secret I've been scuffling a little bit the past few weeks,'' Moore said. ''Just the game of baseball, man, it's tough and, yeah, definitely tonight's a big boost to the confidence and a big boost to how I know that I can play at this level and moving forward. It's definitely a statement.''
The Mariners overcame Flexen's early struggles that gave the Angels a 2-0 first-inning lead on RBIs from Rendon and Jared Walsh. Ohtani's homer put them ahead 3-2 in the third.
Tom Murphy's fourth-inning solo homer ended the night for Angels starter Andrew Heaney (1-2). He had given up just one homer in 20 2/3 innings this season.
''I was as surprised as you are,'' Angels manager Joe Maddon said of Heaney's homer struggles. ''He definitely made some good pitches.
''It was kind of confusing.''
Murphy and J.P. Crawford added RBI doubles in the eighth.
Moore ''and Murph have both been grinding,'' Servais said. ''They've taken more (practice) swings in the last two weeks than anybody on the team.''
Angels: Maddon says a sore spot on RHP Ohtani's finger is unlikely to derail his scheduled start Monday when LA hosts Tampa Bay. ''It's kind of a nonissue, and I hope it stays that way,'' Maddon said. . The team is looking for an opening on the roster to bring back OF Juan Lagares (calf), who's been on the injured list since April 13.
Mariners: Servais isn't sure how long 1B Evan White will on the bereavement list due to the death of his grandfather. Complicating matters are the quarantine procedures the Gold Glove winner must go through before he can rejoin the team. C Jacob Nottingham, acquired Wednesday on waivers from Milwaukee, replaces him on the roster.
Angels: RHP Griffin Canning (1-2, 8.40) returns to the mound after giving up a season-high six runs in a loss at Houston on Saturday.
Mariners: RHP Ljay Newsome (1-0, 1.69) takes injured ace Marco Gonzales' (left forearm strain) spot in the rotation. Newsome had been coming out of the bullpen in long relief before the injury.
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