Severino gave up four hits and struck out four. He got out of a two-on, two-out jam in the first by striking out Desmond Jennings.
"He has composure out there," Yankees manager Joe Girardi said. "Sometimes you forget he's 22. When you look at David Price, the way he came up. He kind of started really in the bullpen, thrown right in the World Series in the bullpen. (Clayton) Kershaw, a lot of poise. I was around a Greg Maddux when I was a young player. There was a ton of poise. He knew exactly what he wanted to do and I feel like Sevie is the same way."
Severino is attempting to secure a spot in the rotation after going 5-3 with a 2.89 ERA in 11 starts during his first major league season last year.
"I see Severino being one of the best pitchers in the game," Yankees right fielder Carlos Beltran said. "He just needs experience."
Moore, aiming for his first healthy season since undergoing elbow ligament replacement surgery in April, 2014, allowed two hits and had three strikeouts. The lefty retired his final nine batters after allowing a two-out single in the first to Beltran.
"Matt Moore was outstanding," Rays manager Kevin Cash said. "We've talked about it all spring about how he's been a bright spot for us."
Beltran was the lone expected opening day starter in a Yankees' lineup, which included top prospects Gary Sanchez and Jorge Mateo. Beltran singled in two at-bats against Moore.
Yankees: Severino threw 43 of 59 pitches for strikes.
Rays: Moore gave up a leadoff homer to Boston's Mookie Betts on Monday before retiring his next six batters in his first start.
"Compete, see what I got and go from there," Moore said.
Yankees: LF Brett Gardner will take part in a simulated game Sunday and is expected to play in Wednesday's game against Toronto. He hasn't played since bruising his left wrist in last year's AL wild-card loss to Houston. ... INF-OF Dustin Ackley is out with mild quadriceps tightness.
Rays: RF Corey Dickerson left in the fifth with a bruised left forearm after getting by a pitch. Cash said no X-rays were taken and that Dickerson should DH Sunday. ... RHP Matt Andriese was scratched from his start Sunday due to left abdominal tightness.
CUT FOR A CURE
For the fifth consecutive year, Rays players, coaches and front office staff had their heads shaved as part of the Pediatric Cancer Foundation "Cut for a Cure." Ava Raab, a 7-year-old cancer survivor from Seffner Florida, threw out the ceremonial first pitch.
Rays: RHP Erasmo Ramirez will start a split-squad game against Boston Sunday. RHP Taylor Guerreri will pitch for the other squad against Toronto.