NEW YORK -- Even after the New York Yankees embarked upon the franchise's biggest rebuilding project in a generation, general manager Brian Cashman and manager Joe Girardi spoke optimistically Monday afternoon about the Yankees' chances of remaining a factor in the American League playoff race.

For one game, at least, the Yankees made Cashman and Girardi look prescient.

Starlin Castro's sacrifice fly in the top of the 10th inning gave the Yankees a wild 6-5 win over the New York Mets in the first "Subway Series" game of the season at Citi Field.

The go-ahead RBI by Castro capped a whirlwind day for both teams, who have similar records despite vastly different approaches to the trade deadline that arrived Monday at 4 p.m.

The reigning National League champion Mets (54-51), who entered Monday 2 1/2 games behind the Miami Marlins in the race for the second wild-card spot, acquired outfielder Jay Bruce from the Cincinnati Reds for two prospects, and they obtained left-handed pitcher Jonathon Niese from the Pittsburgh Pirates in exchange for left-hander Antonio Bastardo.

"We're certainly adding a big bat to our lineup, which makes us that much better," Mets manager Terry Collins said before the game.

The Yankees (53-52), who were swept by Tampa Bay over the weekend to enter Monday 5 1/2 games behind the Boston Red Sox in the race for the American League's second wild card, completed their fire sale by trading Carlos Beltran to the Texas Rangers for three prospects and sending Ivan Nova to the Pittsburgh Pirates for two players to be named later.

Both Beltran and Nova were informed of the deals after arriving at Citi Field.

"Everybody was a little bit down here," Castro said. "That's a good win to start off with. The guys, they're not here anymore. We (need to) keep focused and try and win games."

Cashman began the rebuilding process July 25, when he dealt closer Aroldis Chapman to the Chicago Cubs for four players. It continued Sunday, when left-hander Andrew Miller, who replaced Chapman at closer, was traded to the Cleveland Indians in another 1-for-4 deal.

The retooling marks the first time the Yankees have traded stars near the deadline since 1989, when Rickey Henderson was dealt to the Oakland Athletics. The Yankees made the playoffs 18 times in the previous 21 seasons.

"That run of contention, of being legitimately considered a team that could win a championship on a year-in, year-out basis, has gone on for a long time," Cashman said before the game. "From my perspective, no shame in anything that we've tried to adjust today."

Neither Cashman nor Girardi wanted the trades to be viewed as a sign the Yankees were completely giving up on the season.

"We could be a team that all of a sudden doesn't start dipping in the standings, as this weekend we just came out of created," Cashman said.

Said Girardi beforehand: "I believe that you can win with the players in that room. Did we lose some really good players? Absolutely. Some people are probably going to think that I'm delusional. But there's no reason to put on the uniform if you don't think you can win."

Both teams looked primed to win Monday, when there were two ties and three lead changes. A homer by Wilmer Flores gave the Mets a 1-0 lead in the second before the Yankees scored once in the fourth, when Jacoby Ellsbury raced home on a wild pitch, and twice in the fifth on consecutive RBI doubles by Brett Gardner and Ellsbury.

Rookie shortstop Matt Reynolds hit a three-run homer in the bottom of the sixth but the Yankees tied it in the eighth on Didi Gregorius' two-run single. One run apiece was charged to left-hander Jerry Blevins, who allowed two runs in July, and right-hander Addison Reed, who entered Monday with a career-long 16 1/3-inning shutout streak.

"We like to get in that situation every night when we get the lead with those guys coming into the game," Collins said. "We'll take our chances."

The Mets nearly tied or won the game in the bottom of the 10th against new Yankees closer Dellin Betances, who wriggled out of a first-and-third, one-out jam to lock down his first save and preserve the win for Adam Warren (4-2).

"It's going to be tough without our guys in here," said Yankees left-hander CC Sabathia, who allowed five runs on eight hits and three walks while striking out five over 5 2/3 innings. "But we have the guys in here to battle and try to get back in this thing."

Seth Lugo (0-1) took the loss for the Mets. Right-hander Logan Verrett gave up three runs on four hits and three walks while striking out two over five innings.

NOTES: Neither OF Jay Bruce, acquired from Cincinnati, nor LHP Jonathon Niese, acquired from Pittsburgh, arrived in time to be added to the Mets' 25-man roster Monday. ... To replace OF Carlos Beltran (traded to Texas), RHP Ivan Nova (Pittsburgh) and LHP Andrew Miller (Cleveland), the Yankees added RHP Tyler Clippard, whom they acquired from Arizona on Sunday, to the 25-man roster while recalling OF Ben Gamel and RHP Nick Goody from Triple-A Scranton/Wilkes-Barre. The Yankees played a man down Sunday following Miller's trade to the Indians.