ST. PETERSBURG, Fla. -- The success story of Yankees rookie Gary Sanchez added another chapter Tuesday night as the catcher hit a three-run homer in the seventh, helping rally New York to a 5-3 victory over the Tampa Bay Rays at Tropicana Field.

"He's meant a lot since he's been up here, offensively and defensively," manager Joe Girardi said after Sanchez's 17th home run in 44 games, his first to take the lead in the seventh or later. "You can change games in a lot of different ways. It's kind of fitting that he got the big hit."

The Yankees (78-72) bounced back from a four-game sweep against Boston that had them losing seven of eight games and falling out of serious wild-card contention. The Rays (64-86) had won four of six coming in, but couldn't play the spoiler role they've played with the rest of the American League East in the past month.

Sanchez's 17 home runs are the most by a Yankees rookie since Alfonso Soriano in 2001. They're also tied for the most home runs in a player's first 44 career games in the last century, equaling the Boston Braves' Wally Berger in 1930. He's hit home runs in three straight games and has six in his last 11 contests.

"Obviously, teams have a little better book on him and he's learned how to adjust to what teams are trying to do to him," Girardi said. "It says a lot about him."

Tampa Bay had a 2-1 lead in the seventh thanks to a strong start from lefty Drew Smyly, who held the Yankees to four hits in six innings. Reliever Brad Boxberger matched that in the seventh alone, giving up singles to Ronald Torreyes, Mason Williams and Brett Gardner, the last tying the game at 2-2. With two outs, Rays pitching coach Jim Hickey visited the mound and opted to keep Boxberger in, and Sanchez crushed the next pitch for a 5-2 lead.

"We let one get away from us a little late today," Rays manager Kevin Cash said. "They pieced together some solid at-bats, got three singles to score and tie it back up, and obviously Sanchez with the big three-run home run to separate the game there."

Asked if he was surprised the Rays chose to pitch to Sanchez with first base open, Girardi was polite.

"That's not my job to decide what they're going to do or not do, so I'll choose not to comment on that," he said.

The Rays scored a run in the eighth when Logan Forsythe tripled off the wall in left field and scored on a wild pitch, cutting the lead to 5-3. Yankees closer Dellin Betances pitched a scoreless ninth for his 12th save of the season.

Smyly, who came in with a 2-0 record and 2.08 ERA against the Yankees this season, was sharp again Monday, holding New York to one run on four hits through six innings.

"I didn't want him to go any deeper at all. That's why I made the decision," Cash said of pulling Smyly after 87 pitches. "I thought he had done his job and given us a chance to win. It made it pretty easy to set up the bullpen, and it didn't work."

Smyly worked out of jams in the first and sixth. Aaron Hicks singled and Billy Butler doubled in the first, but with two in scoring position, Mark Teixeira popped out to third to end the inning. In the sixth, Sanchez walked and Butler again doubled, but this time the Rays walked Teixeira to load the bases with two outs. Smyly came through again, getting Didi Gregorius to pop out to left field and preserve a 2-1 lead.

The Rays were held in check for the most part by Yankees starter Michael Pineda, but scored two runs in the third with a two-out rally. Logan Forsythe singled and Evan Longoria reached on an infield single where Donovan Solano's throw to first was high, pulling Teixeira off the base. That kept the inning alive for Brad Miller, who tripled off the wall in left-center to score both runners for a 2-0 Rays' lead.

The Yankees answered in the fourth on a solo home run by Teixeira, his 13th of the season, to make it 2-1.

NOTES: Two Rays players underwent season-ending surgeries Tuesday. OF Steven Souza had surgery on his left hip in Nashville, Tenn., and 1B Logan Morrison had surgery on his left wrist in Orlando, Fla. That's three season-ending surgeries in two weeks, following SS Matt Duffy (heel). ... UTIL Nick Franklin had an MRI on Sunday that showed a moderate strain of his left hamstring. ... INF Donovan Solano made his Yankees' debut Sunday, the 53rd player to suit up for New York this season. The most the Yankees have used in a season is 58 in 2014, with 56 playing last season. ... DH/1B Billy Butler had hit safely in his first five games with New York, going 6-for-14 with a home run, two doubles and four RBIs. He's the first player to open his Yankees' career with a five-game hit streak since Chase Headley had eight straight in 2014.