The Rays' 6-3 win Tuesday in New York City also was the Yankees' first loss this season at Yankee Stadium.
Snell allowed four hits and three runs in five innings to move to 2-0 on the season. The Rays touched up Yankees starter Masahiro Tanaka for eight hits and six runs in four innings.
Rays catcher Michael Perez drew first blood with an RBI single in the top of the third frame before Lowe stepped to the plate in the same inning with two runners on base.
The Rays utility man took a Tanaka slider for a ball before he eyed a 1-0 fastball. Lowe belted the offering to center field for a 424-foot homer. The blast traveled 106 mph and left the field in 4.9 seconds, according to Statcast.
The Rays took the 4-0 lead into the next inning before they scored for a fifth time on a passed ball. Gary Sanchez then put the Yankees on the scoreboard with a solo homer in the bottom of the fourth inning. Meadows then stepped up to the plate to lead off the fifth frame.
The Rays left-fielder was the final batter Tanaka faced before he was removed from the game. Tanaka earned a called strike on Meadows before he fell behind 2-1 in the count. Meadows then mauled his fourth pitch of the exchange for a 424-foot homer to center field.
Yankees first baseman Luke Voit hit his eighth home run of the season in the bottom of the fifth inning. The two-run blast traveled 393 feet before it went over the left-field fence.
Rays relief pitchers Pete Fairbanks, Diego Castillo, Nick Anderson and Chaz Roe combined to shut out the Yankees over the final four innings to secure the victory. Roe earned his first save of the season.
Meadows went 2 for 4 with two runs scored and an RBI in the win. Lowe went 1 for 3 with three RBIs, a run scored and a walk for the Rays. Voit went 1 for 3 with two RBIs, a run scored, a walk and a strikeout for the Yankees.
The Yankees (16-7) host the Rays (15-9) at 7:05 p.m. EDT Wednesday at Yankee Stadium.