NEW YORK -- For a team languishing in last place, the future looks awfully bright in Boston.
The 21-year-old Bogaerts drove in two runs and finished a triple short of the cycle. He and Betts, born six days apart in October 1992, became the first pair of Red Sox rookies to homer at Yankee Stadium in the same game since Dick Gernert and Faye Throneberry on Aug. 9, 1952.
"This season definitely has not been the way that we all wanted, we all expected it to be. But there's a lot of talent coming up and hopefully we can blend in together and have a good future," Bogaerts said.
Betts had three hits and slumping Mike Napoli added two sacrifice flies for the defending World Series champions, who have won eight of 11 on the road.
"It's fun watching what these guys did with the bats," Kelly said.
A furious Brett Gardner got ejected on a frustrating -- and sometimes embarrassing -- night for the Yankees, who fell five games out of a playoff spot. They've lost five of seven following a five-game winning streak.
Rookie right-hander Shane Greene (4-2) was hit hard and chased in the third inning. New York had won his previous five starts.
Staked to a 6-0 lead, Kelly (1-1) gave up Martin Prado's leadoff homer in the third and pitched through all sorts of trouble in a two-run fifth. He went 6 2/3 innings in his sixth start for Boston since being acquired at the July 31 trade deadline from St. Louis, where he was 2-2.
Cespedes singled and Napoli walked in front of Nava's third home run in the third. Two batters later, Bogaerts sent an opposite-field drive to right-center for his first home run since July 29 against Toronto.
The shortstop, who entered hitting .224, has seven hits in his last three games. He was activated Saturday from the seven-day concussion disabled list.
"Looks like a few days down rejuvenated him some," manager John Farrell said. "It's good to see him bounce back."
Embarrassing baserunning cost the Yankees when they threatened to get back in the game after Brian McCann beat the shift with a bunt single in the fifth.
Prado hit a drive over Cespedes' head in left field, and the ball short-hopped the wall. Carlos Beltran, however, got a bad read and thought the ball might be caught. So he headed back toward second before reversing course and jogging into third.
McCann had to hold up at second as Prado charged unaware toward the bag. He never even saw McCann standing on second until he was a few steps away. That left Prado trapped between bases, and he soon gave up in a rundown.
"It's tough because we gave them one out," manager Joe Girardi said. "It looked like we were getting to him, and that was a big out."
Kelly walked his next two batters, forcing in a run, and Jacoby Ellsbury lined out with the bases loaded. Derek Jeter's infield single -- he was initially called out before a replay review -- made it 7-3.
Kelly then threw a called third strike past Gardner, who flipped his bat in disgust and fired down his helmet with two hands. He was immediately ejected by plate umpire Tim Timmons.
"I saw a replay of it and obviously it was outside -- just where I thought it was," Gardner said. "Felt like I got the bat taken out of my hands there really in a pretty big situation. The pitcher was on the ropes and I just let my emotions get the best of me."
McCann homered in the ninth off Koji Uehara, who had been rested since Aug. 25.
Yankees: Prado was pulled in the ninth with a tight left hamstring and sent for tests. ... Ellsbury led off after being held out of the starting lineup for two games because of a sore left ankle. Gardner batted third for the first time in his career, according to STATS, and struck out all three times up. ... RHP David Phelps (elbow inflammation) threw 25 pitches in a bullpen session and is scheduled to throw 35 in another one Friday before a simulated game Sunday.
Red Sox RHP Anthony Ranaudo (3-0, 4.50 ERA) was recalled from the minors and expects about 30-40 family members and friends in the stands when he makes his fourth major league start Wednesday night. Ranaudo grew up nearby in New Jersey and said he went to countless games at the old Yankee Stadium.
"I can't even describe how excited I'm going to be," Ranaudo said, wondering if he would be able to fall asleep Tuesday night. "There's going to be a lot of emotions."
Ranaudo beat the Yankees in his big league debut Aug. 1 at Fenway Park. Hiroki Kuroda (9-8, 3.88) pitches for New York.
Bogaerts became the youngest Red Sox player with four hits in a game since 21-year-old Glenn Hoffman on May 3, 1980, at Kansas City.
UP IN THE AIR
New York recorded only one out on the ground and did not have an assist.
NICE TO MEET YOU
Making his first appearance against the Yankees, Kelly matched a career high with six strikeouts in his first win since July 19 against the Dodgers. He had gone seven outings without a victory.