Happ and four relievers combined on a two-hitter, Cameron Maybin contributed with his bat and glove, and the Yankees beat the Seattle Mariners 3-1 Thursday night.
"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.
The Mariners also are facing a series of injury problems involving Dee Gordon, Edwin Encarnacion and Dylan Moore.
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 (championship rings) 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 (mlb championship rings) 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.
Adam Ottavino, Tommy Kahnle and Zack Britton each threw a scoreless inning. Aroldis Chapman got his eighth save in nine chances.
Mike Leake (2-4) allowed six hits in seven effective innings.