ST. PETERSBURG, Fla. (AP) Alex Rodriguez enjoyed being overshadowed by a rookie.
The 24-year old Heathcott's second career homer came on his first at-bat in the major's since May 27. He was called up from Triple-A Scranton/Wilkes-Barre on Saturday.
''Just tremendous,'' Rodriguez said. ''You get caught up and I become a fan when you're watching a young kid with so much talent. Big, signature Yankee moment.''
The victory moved the Yankees within three-games of AL East-leading Toronto.
''To be able to do it with two outs in the ninth, it was special,'' New York manager Joe Girardi said.
In the bottom half Tampa Bay snapped a scoreless tie, ending its 21-inning run drought on Logan Forsythe's RBI double.
The Yankees, though, rallied in the ninth. Down to their last out, Brett Gardner was walked by Brad Boxberger (4-10) on four pitches and stole second. Then Rodriguez tied Craig Biggio for 21st place all-time with his 3,060th hit.
Heathcott homered after Brian McCann was intentionally walked, setting off a raucous celebration in the New York dugout, A-Rod leading the way.
''It was awesome,'' Heathcott said.
Ramirez allowed just the one hit, walked two and had six strikeouts in 7 2-3 innings.
''I definitely checked it (the no-hitter) out in the fifth and sixth, but I tried to stay away from that and stay focused on the next hitter and what pitch I'm going to use,'' Ramirez said.
CC Sabathia had a strong start for the Yankees, giving up three hits over 6 2-3 scoreless innings. He worked out of a bases-loaded, one-out jam in the second.
''You just look at our dugout, the way they reacted, it's the biggest hit of the season,'' Sabathia said of Heathcott's blast.
New York is 3-54 when trailing after eight innings.
The Yankees had two baserunners through the seventh. Rodriguez walked with two outs in the fourth and Gardner drew another walk to start the seventh.
Gardner was doubled off second after Mikie Mahtook made a leaping catch into the right-field wall on Brian McCann's drive.
Yankees: Girardi said CF Jacoby Ellsbury, in a 1 for 29 slide, is physically fine. ''He feels pretty good,'' Girardi said.
Rays: Reliever Jake McGee (left knee) threw his third bullpen and will need at least one more before getting in a simulated game. ''We'll see how the knee bounces back tomorrow,'' he said
Matt Garza has the only Tampa Bay no-hitter, beating Detroit 5-0 on July 26, 2010.
The Yankees were last no-hit when Houston used six pitchers in an 8-0 victory June 11, 2003. New York was last no-hit by a single pitcher when Baltimore's Hoyt Wilheim beat Don Larsen 1-0 on Sept. 20, 1958.
NHL coaching great Scotty Bowman was at the game. He has been a part of 14 Stanley Cup-winning teams, including a record nine as coach. A senior adviser with the Chicago Blackhawks, he will be heading to Notre Dame late this week for the start of training camp with the defending NHL champions.
Yankees: Girardi said RHP Adam Warren (6-6, 3.29) will be able to throw around 65 pitches in a spot start Tuesday night.
Rays: RHP Jake Odorizzi (7-8, 3.21 ERA), Tuesday night's starter, has the second lowest run support in the AL.