The Yankees broke the game open in the fifth inning when Rice hit his first career grand slam after Mitch Spence had relieved an ineffective Severino.
The former Yankees starter struggled in his first career start against his former team, matching a career worst with eight earned runs allowed in four-plus innings.
Ryan Yarbrough (1-0) allowed two runs in five innings in his second start of the season to get the win.
JJ Bleday homered for the A's, who fell to 8-13 at home this season.
Key moment
The Yankees took control of the game in the second inning with an RBI single by Anthony Volpe, a bases-loaded walk by Oswaldo Cabrera and a run-scoring groundout by Jorbit Vivas. Judge then delivered the big hit with a line single that drove in two runs, giving him 39 RBIs this season.
Key stat
Paul Goldschmidt had three doubles and has now hit safely in all 19 road games he has played this season. The only other Yankees to do that are Derek Jeter with 23 straight to open the 2007 season and Jack Lelivelt with 21 in 1912.
Up next
The Yankees open a three-game series in Seattle on Monday night with RHP Clarke Schmidt (0-1, 4.79) set to start. The A's start a three-game series in Los Angeles against the Dodgers on Tuesday night with LHP Jeffrey Springs (4-3, 4.81) set to start the opener.
___
AP MLB: https://apnews.com/MLB
Credit: AP
Credit: AP
Credit: AP
Credit: AP
Credit: AP
Credit: AP