MESA, Ariz. — Could the A’s have a stealth contender in the fifth-starter race?

Daniel Gossett, who pitched at three levels of the A’s system last year, got the start Sunday against the Angels when the team decided to rearrange its pitching plans in the wake of Sonny Gray’s departure from the World Baseball Classic. Gossett worked two scoreless innings in the A’s 5-3 loss to the Angels, walking two.

“He impressed everybody in the organization last year, so in talking about that fifth starter, who knows?” manager Bob Melvin said. “This is a nice little feather in his camp to start a game against a division team, our opener at home.”

Gossett, 24, went 10-6 with a 2.69 ERA combined at Class A Stockton, Double-A Midland and Triple-A Nashville last year. He led Oakland’s system with 151 strikeouts.

One key for Gossett last year: adding a cutter to his repertoire, which already included a fastball, curveball and changeup.

“The cutter really put Daniel over the edge,” said Ryan Christenson, who managed Gossett in Midland. “I talked to a lot of the third basemen and shortstops from the other team and they couldn’t speak highly enough about Daniel’s stuff. He’s getting better command of both sides of the plate, and there’s something about that cutter, something late about it that’s really wicked to the hitters.”

Minor-league instructor Gil Patterson helped Gossett with the pitch. “It was just a different look, and I had some success with it,” said Gossett, who was a second-round pick in 2014 from Clemson, where he played with A’s bullpen catcher Phil Pohl. Gossett next will see action Friday.

Another fifth-starter hopeful, right-hander Paul Blackburn, worked two scoreless innings with a walk and a strikeout.

Briefly: Ryon Healy (minor quad strain) was cleared to play first base against the Giants on Monday. … Outfielder Jake Smolinski has been sidelined by a shoulder injury. … Fifth-starter candidate Frankie Montas will throw another bullpen session before appearing in a game. … Catcher Matt McBride is out with a lat strain, leaving the A’s thin in catchers, with Ryan Lavarnway departing Monday to join Israel’s WBC team. Melvin said that will result in more opportunities for Sean Murphy, who was drafted in June.

Susan Slusser is a San Francisco Chronicle staff writer.

Angels 5, A’s 3

Notable: Catcher Josh Phegley threw out Jefry Marte trying to steal second in the second. ... Alejandro De Aza, signed as a minor-league free agent, was hit by a pitch in the first and tripled and scored on a double by Mark Canha in the third. … Minor-leaguer Aaron Kurcz gave up two hits, two walks and three runs in the seventh. … Triple-A Nashville outfielder Jaycob Brugman had an RBI single in the seventh. … Shortstop Franklin Barreto had two singles.

Quotable: “It felt a little foreign to be out there again.” — Phegley, who missed the final three months of last season after knee surgery.

Monday’s game: A’s vs. Giants at Scottsdale Stadium, 12:05 p.m. Radio: 680

Susan Slusser