The slumping Correa, who earlier hit an RBI double and made a sensational play at shortstop, connected for an opposite-field shot to right off J.A. Happ.
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Correa watched the ball sail, then held up one finger as he rounded the bases. As he approached home plate, he tossed his helmet as if shooting a basketball at the crowd of teammates waiting for him.
Game 3 is Tuesday afternoon at Yankee Stadium. Gerrit Cole, who is 18-0 in his last 24 starts and led the majors in strikeouts, starts for the Astros against Luis Severino.
"The game of baseball, it's a beautiful game," Correa said.
Correa was sidelined for a while late this year because of back trouble. The All-Star began the day in a 3-for-22 skid this postseason.
The Yankees tied a League Championship Series record by using nine pitchers. The eight relievers had permitted only one run and two hits with 11 strikeouts before Correa homered, ending a game that took four hours, 49 minutes and ended right around midnight.
Houston's five relievers combined for 4 1/3 innings of one-hit shutout ball after taking over for Justin Verlander. Going into this best-of-seven series, the Yankees were considered the better team in the bullpen - the Astros amply held their own in this one.
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Gary Sánchez struck out looking to end the Yankees 11th with runners on first and second. The pitch appeared outside - it came right after he swung and missed with two strikes, but was ruled a foul ball.
Aaron Judge hit a two-run homer off Verlander that put the Yankees ahead 2-1 in the fourth. George Springer tied it in the fifth with a home run off reliever Adam Ottavino.
Correa kept it tied at 2 in the sixth. With runners at first and second, and on the move on a full-count pitch with two outs, Brett Gardner hit a hard grounder that bounced off second baseman José Altuve for a single.
The ball bounded away and Correa quickly retrieved it and threw a strike to catcher Robinson Chirinos, who tagged out the sliding DJ LeMahieu.
Correa hit an early RBI double off James Paxton.