Bird hit a three-run homer on Tuesday during the Yankees' 6-5 loss to Baltimore.
His grand slam broke open the Wednesday game during a five-run third inning that gave the Yankees control.
New York starter Sonny Gray (6-7) turned in one of his best performances of the season. The right-hander threw six shutout innings, allowed only three hits and snapped a personal three-game losing streak.
Gray also struck out eight and walked just one.
Baltimore starter Dylan Bundy (6-9) has been hurt by the long ball at times this season, and the Bird grand slam continued the trend. Bundy allowed five runs on five hits in four innings and needed 91 pitches to get that far.
Bundy has lost his past two starts since coming off the disabled list after recovering from a sprained ankle. He has given up 20 homers in 103 1/3 innings this season.
The Orioles had a chance to take the lead when they put runners on second and third with one out in the second inning, but Gray retired the next two batters and kept the game scoreless.
New York jumped on top in the third. Giancarlo Stanton (4-for-5, two RBIs) made it 1-0 with an RBI single, and later in the inning, Bird sent a shot that hit the right field foul pole for a grand slam and a 5-0 lead.
New York added another run in the sixth when Tyler Wade led off with a homer off Mike Wright Jr. It was Wade's first major league homer.
Austin Romine made it 7-0 with his solo homer in the seventh against Jhan Marinez, who was making his Orioles debut. The Yankees got a run on an error in the eighth, and Stanton added an RBI single in the ninth.
--Field Level Media