"He was pretty intense throughout that game," manager Aaron Boone said about his starter.
The Yankees won for the fourth time in five games. They now head to Tampa Bay to play the AL East-leading Rays for the first time this year.
Knocked around by Minnesota in his previous outing, Happ was in charge, allowing one single while pitching into the sixth inning.
"I think I just held some frustration from that last start," he said.
Domingo Santana homered with two outs in the ninth for Seattle, which has dropped nine of 11.
Gordon exited early after being hit on the right wrist by Happ's pitch. The leadoff man shouted while leaving the field, cursed postgame while explaining what happened and wasn't sure if he'd miss any time.
"It's the second time he threw up and by my head. So, you got to get the ball down. If you can't throw that pitch, don't throw it. I got a family," Gordon said.
Moore, also nursing a sore wrist after being hit by a pitch Wednesday, took over for Gordon at second base. But Moore needed to leave when the injury acted up.
With the Mariners running out of options, Encarnacion shifted from first base to second in the eighth. Playing the position for the first time in his career, the slugger hurt his left wrist diving for DJ LeMahieu's leadoff grounder.
Checked by a trainer, Encarnacion stayed in the game.
"I'm thinking, what else can go wrong? I was thinking, hopefully he's OK," Moore said. "Obviously, you don't want anyone else to get hurt. It's one of those things where everyone's got to do the best they can."
Said manager Scott Servias: "We may need to get some extra help ... and see what we do roster-wise."
Maybin flared a two-out RBI double in the second and made a sliding catch on Ryon Healy's fly to right to begin the seventh.
Gio Urshela added a two-run single in the eighth, an inning after entering for defense.
Happ (2-3) gave up a single by Tom Murphy in the fifth and struck out seven. The lefty has been hurt by homers, particularly in the Bronx, but shut down the club that leads the majors in long balls.
Moore drew a leadoff walk in the sixth -- curiously, he bluffed a bunt on a 3-2 pitch that was borderline high. That finished Happ and he chirped at plate umpire Ed Hickox as he walked off, showing how Moore squared around.
Mike Leake (2-4) allowed six hits in seven effective innings.
Yankees RHP Danny Farquhar is scheduled to pitch Friday for the first time at extended spring training. The 32-year-old reliever collapsed in the Chicago White Sox dugout in April 2018 because of a ruptured aneurysm and brain hemorrhage. He signed a minor league deal with the Yankees in the offseason and pitched three times in spring training, allowing six runs and five walks in two innings. He's been building shoulder strength at the team's complex in Tampa, Florida.
The Yankees signed LHP Nestor Cortes Jr. to a major league contract and selected him to the 25-man roster. The 24-year-old Cuban made his debut last year with Baltimore. RHP Dellin Betances (shoulder impingement) was transferred from the 10-day injured list to the 60-day IL.
Yankees: OF Aaron Hicks (back strain) is expected to rejoin the Yankees on Monday. He'll play Triple-A games this weekend. ... SS Didi Gregorius plans on starting live batting practice next week and remains on target to DH in an extended spring training game around May 20. "It's a slow process. Can't wait to get going," he said in Florida.
Mariners: Servais will miss the first two games of Seattle's weekend series in Boston to attend his daughter's college graduation. RHP Erik Swanson (1-3, 4.94 ERA) starts the opener at Fenway Park.
Yankees: RHP Domingo German (6-1, 2.35) faces Rays RHP Tyler Glasnow (6-0, 1.47) -- they're among the pitchers tied for the major league lead in wins. The Yankees take a depleted lineup into Tropicana Field. Assessing the matchup, Boone said, "I don't really see it as where we stack up."
AP freelance writer Mark Didtler contributed to this report.
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