ST. PETERSBURG, Fla. -- Tampa Bay Rays starter Jake Odorizzi took a no-hitter into the seventh, but the Yankees' only hit was a two-run home run by Starlin Castro, enough for New York to pull out a 2-1 victory on Sunday at Tropicana Field.

The Yankees hadn't won a game while getting exactly one hit since July 1914.

The Yankees (24-25) took two of three from the Rays, getting another strong start from Nathan Eovaldi (6-2), who won his fifth straight start. The Rays (22-26) outhit the Yankees 6-1 but took their seventh loss in nine games as they head into a 10-game road trip.

The Yankees' first hit -- with one out in the bottom of the seventh -- also gave them a 2-1 lead, as Castro followed a walk to Brett Gardner with a two-run home run to left-center, his seventh home run of the season. Odorizzi stayed in for the final two outs of the inning, leaving the game after throwing 108 pitches.

The Yankees' bullpen took over from there with three perfect innings of relief: Dellin Betances struck out two in a perfect seventh, and Andrew Miller struck out the side in the eighth. Aroldis Chapman pitched a 1-2-3 ninth for his seventh save, striking out two. Eovaldi held the Rays to one run on six hits in his six innings for the win.

Odorizzi was perfect through five innings, striking out five Yankees batters and going for what would have been the first perfect game and just the second no-hitter in Rays history. Matt Garza had the only one, against the Tigers in July 2010.

Odorizzi allowed his first baserunner in the sixth, as Yankees first baseman Dustin Ackley reached when shortstop Brad Miller double-clutched a ground ball and was late with the throw. The Rays challenged the safe call, but it was upheld upon review. The Rays followed with a double play to keep the no-hitter intact and keep Odorizzi facing the minimum through six innings.

The Rays didn't do much offensively either, but got on the scoreboard in the third inning, as Brandon Guyer got a single up the middle, advanced on a fielder's choice and wild pitch and scored on an RBI single by Evan Longoria for a 1-0 lead. Eovaldi gave up just four hits in the first five innings.

The Rays had a chance to extend their lead in the sixth, leading off with singles from Steve Pearce and Logan Morrison. After a two-out walk to load the bases, Eovaldi got Curt Casali to pop out to first to end the threat.

NOTES: Rays C Hank Conger had three extra-base hits Saturday and threw out a runner trying to steal, the first time any AL catcher has done both in the same game since the Orioles' Matt Wieters in August 2012. ... Yankees RHP Nathan Eovaldi came in with back-to-back starts of at least six innings with two or fewer hits -- the only other AL pitcher to do that this season is Chicago's Chris Sale, and only one other Yankees pitcher (Freddy Garcia, 2011) has done it since 2000. ... Rays SS Brad Miller had a "triple double" in Saturday's game, hitting both a triple and double, something he has done three times this season. Nobody else in the majors has done it more than once.