Andrew Heaney showcases the heater in a one-hitter against Royals

Andrew Heaney walked through the clubhouse Tuesday afternoon with a backpack in one hand and a cheesecake in the other, the dessert baked by his wife to mark the Angels left-hander’s 27th birthday.

How sweet it was: Heaney could have lighted one candle for every out he recorded in the best game of his four-year career, a one-hitter to beat the Kansas City Royals 1-0 in Angel Stadium.

With virtually no margin for error on a night his offense literally stole its only run, Heaney struck out four and walked one. His only blemish was a clean one-out single to left in the fifth inning by Hunter Dozier.

Mixing a fastball that hit 95 mph in the ninth inning with pinpoint location of his curve and changeup, Heaney threw a career-high 116 pitches, 81 for strikes.

It was his first complete game as a professional on any level, giving Heaney the rare chance to hug his catcher after recording the 27th out.

“It was fun,” Heaney said. “You want to shake your catcher’s hand, then go shake hands with your teammates. It’s something I’ll never forget.”

Heaney’s gem was the first one-hitter for the Angels since Ervin Santana on June 16, 2012, against Arizona and the first by an Angels left-hander since Chuck Finley on May 26, 1989, at Boston.

“The quality of his pitches, maintaining stuff, pitching with his back against the wall the whole game and finishing it off … his stuff in the ninth inning was as good as it was all game,” manager Mike Scioscia said. “That was a masterpiece.”

The taut game might have helped Heaney.

“I think it keeps you locked in,” Heaney said. “It’s a one-run game, one guy can tie it up, change the whole game. You’re throwing a 2-0 fastball, trying to put it where you want to, and if you don’t, they can make you pay.”

Heaney, who sat out 2016 and four months of 2017 because of elbow ligament-reconstruction surgery, had 105 pitches through eight innings. There was no doubt he was pitching the ninth.

“There was no exchange,” Heaney said about talking with Scioscia. “He said, ‘You good?’ I said yeah.”

Heaney needed only 11 pitches to retire the side in the ninth, getting John Jay to ground to second, Whit Merrifield to fly to right and Mike Moustakas to ground to third.

“I was just trying to stay on my legs,” Heaney said of the final inning. “There was a little bit of adrenaline, the crowd was going a little bit. It was exciting.”

The third straight win for the Angels contained one potential loss. Shortstop Andrelton Simmons twisted his right ankle while descending the dugout steps before the game and was pulled before the third inning because of a sprain.

Simmons was on crutches and said it’s “possible” he might have to go on the 10-day disabled list.

Simmons is one of baseball’s best defenders and is batting .330 with an .857 on-base-plus-slugging percentage.

The Angels scored their run in the fifth inning with a play that you usually see on a high school or college field. Chris Young singled to center with one out and took third on Michael Hermosillo’s single.

Ian Kinsler flied to right. With an 0-and-2 count on Jefry Marte, Hermosillo took off for second and stopped when catcher Salvador Perez threw through. Young took off from third on the throw and scored before Hermosillo was tagged out in a rundown.

“It was one of those plays where you’re just trying to steal a run,” Young said. “You’re gambling from third base. If he holds onto the ball, I’m just out. It’s a pure gamble, and I’m glad it worked out.”

mike.digiovanna@latimes.com

@MikeDiGiovanna