Bird's home run off Rays reliever Andrew Bellatti hit the 'D' ring of the catwalk -- well over the right-field wall -- and gave the Yankees a 3-1 lead in the top of the ninth.
"(Bird) did a great job," Yankees manager Joe Girardi said. "The double in the (second) off (Chris) Archer -- a very good pitcher -- and then to hit the homer that gave us a 3-1 lead. He's done a really nice job in Mark (Teixeira's) absence."
That was all the Yankees pitching staff would need as Luis Severino (4-3) struck out seven over 5 2/3 innings to get the win. Andrew Miller struck out the side in the ninth for his 34th save.
"I had a rough outing last time and wanted to pitch better," Severino said. "In the bullpen I felt good. I think my changeup and my fastball are working very well. My slider was sometimes working good, sometimes was hanging a little bit, but still working on that."
Archer gave up two runs on four hits in six innings. He struck out seven, giving him 243 strikeouts for the season to break the Rays' record of 239 by Scott Kazmir.
"I'll start with 'If you don't like it, pitch better'," Archer said. "I definitely did everything I possibly could. Mentally, I'm very happy with the process. I backed myself into a bad situation that last inning, walking two and trying to be a little too fine. I'm not going to beat myself up over it. ...but obviously you want to get the team win. It stinks. I was hoping to keep the score 1-0, knowing the starter was still in the game, figuring that we would get one off him and we did. So I'm a little bummed that I gave up that extra run."
Tampa Bay answered with a run in the bottom of the sixth on an RBI double from Steven Souza Jr. that scored first baseman James Loney.
The Rays had a golden opportunity with two outs in the bottom of the seventh when Yankees reliever Dellin Betances loaded the bases on three consecutive walks, but he recovered to strike out Loney on three straight pitches and end the inning.
The Yankees opened a 1-0 lead in the top of the second. Center fielder Carlos Beltran led off the inning with a walk and Bird roped a double into the right-center-field gap that scored Beltran.
"We were facing a guy that's pitched great all season long and has been tough on us," Girardi said. "We made him work hard. We didn't get a ton of runs off him, but we made him work hard and he was out after six innings."
Tampa Bay threatened to tie the score in the top of the fifth when catcher Rene Rivera singled and designated hitter John Jaso doubled to put runners on second and third with one out. But Severino induced a harmless ground ball from right fielder Mikie Mahtook, and third baseman Evan Longoria fouled out to the catcher.
"This came down to a couple of missed opportunities," Rays manager Kevin Cash said. "Severino was tough, man. Fastball that was kind of darting every which way, with the combination of a slider and changeup. Young pitcher, that's the second time we've seen him and he's going to be good. No doubt about it."
NOTES: Yankees manager Joe Girardi has set his rotation for the weekend series against the Mets. RHP Masahiro Tanaka will pitch Friday, with RHP Michael Pineda and LHP CC Sabathia starting Saturday and Sunday, respectively. ... Rays SS Asdrubal Cabrera had an MRI exam and X-rays on his strained left knee Wednesday. Both results came up negative. "They are basically describing it as jumper's knee, kind of a basketball injury," Rays manager Kevin Cash said. "It's more of a knee strain." Cash said Cabrera is day to day. ... Yankees RHP Ivan Nova will move out of the rotation and into the bullpen, Girardi said. Nova has a 6-8 record with a 5.11 ERA in 14 starts. ... Rays LHP Jake McGee and LHP Xavier Cedeno will throw a live batting practice session Thursday. Cash said Cedeno will likely return before McGee.