NEW YORK -- Nights like Tuesday are what the Boston Red Sox have in mind for the future of two of their youngsters.

Shortstop Xander Bogaerts Bogaerts had his first career four-hit game, and center fielder Mookie Betts enjoyed his first career three-hit game and made an outstanding catch, helping the Red Sox to a 9-4 victory over the New York Yankees.

"When you see the likes of what Mookie has done and really when you see what Bogie can do, it's not only exciting, but this is a team that has a lineup that is formidable," said Boston manager John Farrell, whose team is in last place during the defense of its World Series title. "It's much deeper than what it's been, and guys are looking forward to coming to the ballpark every day."

Bogaerts said, "The season has not been the way we all wanted, but there's a lot of talent coming up, and hopefully it can blend in together."

Right fielder Daniel Nava hit a three-run, third-inning home run that extended Boston's lead to 5-0, and he reached base four times. Left fielder Yoenis Cespedes had three hits and his major-league-leading 15th outfield assist as the Red Sox (61-77) won for the fifth time in eight games following an eight-game losing streak.

Those performances were secondary to what Bogaerts and Betts did against the Yankees, who lost for the fifth time in seven games following a five-game winning streak. New York (70-66) dropped five games behind the Detroit Tigers for the second American League wild card.

Bogaerts came within a triple of the cycle. He hit as a monstrous solo homer to right-center field in Boston's four-run fourth, and he added two singles and a double. He became the first Red Sox rookie to have four hits against the Yankees since Jacoby Ellsbury on Sept. 26, 2008, and the first against the Yankees in New York since Hall of Famer Jim Rice on July 27, 1975, at Shea Stadium.

Bogaerts' big night of career also made the 21-year-old the youngest Boston player to have a four-hit game since Glenn Hoffman, who also was 21 when he did it May 8, 1980, at Kansas City.

Bogaerts went a 4-for-34 (.118) over his previous 11 games and missed time due to a concussion.

"This season has been weird one, a tough one," Bogaerts said. "I just keep going to the ballpark and working (on things)."

Betts, who was converted to the outfield earlier this season, had two singles and leadoff home run in the fourth that gave the Red Sox a 7-1 lead. He has multiple hits in four of his last five games and is batting .315 since being recalled from Triple-A Pawtucket on Aug. 18.

"I just saw the ball well today and tried to put some good swings on some good pitches," Betts said. "That's pretty much it."

Betts' home run came right before he robbed New York first baseman Mark Teixeira of a potential extra-base hit with a leaping catch at the warning track. It was his second highlight-reel catch of the season against the Yankees. He robbed Ellsbury of an extra-base hit last month in Boston.

"That's the fun part getting those opportunities," Betts said. "When those opportunities happen, I make sure I try to take advantage of it and go make those catches."

Bogaerts said, "He's like Jackie Bradley, he catches everything."

The performances by Betts and Bogaerts marked the first time two Red Sox rookies hit home runs against the Yankees since Phil Plantier and Bob Zupcic at Fenway Park on Sept. 21, 1991. They were the first Boston rookies to homer in a game at Yankee Stadium since Dick Gernet and Faye Throneberry on Aug. 9, 1952.

The big nights by Boston's two 21-year-olds allowed right-hander Joe Kelly (1-1) to pick up his first win since being obtained from St. Louis. Kelly allowed three runs and five hits in 6 2/3 innings, getting through the later innings by inducing double plays in the sixth and seventh.

The Yankees endured a rough night, typified by left fielder Brett Gardner, who was ejected by plate umpire Tim Timmons in the sixth inning for arguing a called third strike.

"I was frustrated," Gardner said. "I struck out my first two at-bats and felt like I got the bat taken out of my hands there really in a pretty big situation; the pitcher was on the ropes. ... I just let my emotions get the best of me."

The Yankees also ran into an out when second baseman Martin Prado was thrown out trying to stretch a single, and then they lost the utility man in the ninth when he suffered a tight left hamstring that required further testing.

"That's not somebody that we want to lose, he's played extremely well," New York manager Joe Girardi said.

Before getting injured, Prado homered in the third against Kelly. Catcher Francisco Cervelli and shortstop Derek Jeter also drove in runs for the Yankees, while designated hitter Brian McCann homered in the ninth against Boston closer Koji Uehara, who had not pitched since Aug. 25

Rookie right-hander Shane Greene (4-2) had his worst start as a Yankee, allowing six runs and six hits in 2 2/3 innings.

NOTES: The Yankees announced that they will wear a patch with a logo depicting SS Derek Jeter's final season on the left sleeve of their uniforms and cap. It will be worn from Sept. 7 through the end of the year. ... New York RHP Masahiro Tanaka (right elbow) and RHP David Phelps (right forearm) both threw bullpen sessions without difficulties. They will continue their rehabs later this week. ... Boston 2B Dustin Pedroia missed his third consecutive game with concussion-like symptoms. ... Both teams made September call-ups Tuesday. The Red Sox promoted C Dan Butler and RHP Anthony Ranaudo, and the Yankees recalled C John-Ryan Murphy and RHPs Preston Claiborne, Bryan Mitchell and Chase Whitley from Triple-A Scranton/Wilkes-Barre. The Yankees also selected the contracts of LHP Rich Hill, RHP Chaz Roe and OFs Chris Young and Antoan Richardson. They designated OF Zoilo Almonte for assignment and released RHP Matt Daley.