Edwin Encarnacion hit a go-ahead grand slam and the trio of ex-Rockies poured it on in their first reunion with Colorado, helping New York to an 8-2 win.
LeMahieu had two hits and two RBI, Ottavino struck out the side in a perfect relief inning and Tauchman had a career-high three hits, a stolen base and threw out a runner at home plate from left field.
"First time, it's definitely strange," Ottavino said.
Aaron Judge added a two-run homer, and J.A. Happ (8-5) struck out eight while pitching two-run ball over five innings for the Yankees. New York came from behind to win for a fourth straight game and improved to a major league-best 63-33 -- 30 games over .500 for the first time this season. The Yankees lead second-place Tampa Bay by a season-high nine games in the AL East, their biggest division lead since July 2012.
Ryan McMahon, LeMahieu's replacement at second base, hit his 10th homer for Colorado, which has lost 12 of 14. Freeland (2-7) allowed five runs in four innings, striking out six.
Yankees manager Aaron Boone served a one-game suspension from Major League Baseball, a day after going viral for a profane rant aimed at a rookie umpire in a doubleheader opener against the Rays. Boone said the ban didn't surprise him since he made contact with plate umpire Brennan Miller with the bill of his cap.
Bench coach Josh Bard managed in his place. Bard is from Colorado and played for Rockies manager Bud Black in San Diego.
Black was ejected for the first time this season, by plate umpire Doug Eddings after Chris Iannetta's strikeout in the ninth inning.
Stephen Tarpley struck out six over three scoreless innings for his second save, finishing a 17-strikeout night by Yankees pitchers.
"Tonight was a bad night," Black said. "We got to be able to do a better job of putting the ball in play."
Encarnacion lost his grip and whipped his bat past the mound whiffing on strike three in the second inning. His right hand slipped off again on a swing in the third, but his left was strong enough to drive the ball to a fan in the first row in left field for his 12th slam, putting New York ahead 4-2. Freeland allowed consecutive walks that loaded the bases prior to Encarnacion's 29th homer.
"Short porches down the line, that's going to happen sometimes," Freeland said. "But it was really those walks that hurt me."
Colorado traded Tauchman to New York at the end of spring training. Speedy Garrett Hampson tested Tauchman's arm in the second, attempting to score from third on a fly ball. Tauchman one-hopped a 91 mph throw to catcher Gary Sanchez to nab him at the plate.
Tauchman scored for both of LeMahieu's RBI. The latter came on a bold dash from third on a slow roller to third baseman Nolan Arenado, a six-time Gold Glove winner. Tauchman narrowly beat Arenado's feed.
"Happy for Tauchman especially," Ottavino said. "He played an unbelievable all-around game. That team didn't give him a lot of chances, honestly. He came here and put his best foot forward today. I know it meant a lot to him."
"There's a lot of guys I played with for a lot of years over there," Tauchman said. "Some guys on the staff and stuff I had been with since rookie ball."
LeMahieu and Ottavino signed with New York as free agents in the offseason. LeMahieu set a career high with his 67th RBI and increased his batting average to .330 in his first season away from Coors Field. Ottavino pitched a perfect sixth.
Nicknamed LeMachine in New York, the focused, mild-mannered LeMahieu got a different moniker from Charlie Blackmon before the game: "silent assassin." Black said LeMahieu was "a thinking man's player."
Judge also had an outfield assist in right, picking off Arenado in the third after Arenado aggressively rounded second on Ian Desmond's single.
Happ was visited by head athletic trainer Steve Donohue prior to the fourth inning because of a calf cramp on the 91-degree night but remained in the game. He struck out his next two batters.
Rockies: All-Star OF David Dahl was a late scratch due to a bruised left foot. Dahl fouled a ball off his foot during a game against San Francisco on Wednesday night.
Yankees: Cameron Maybin (left calf) took batting practice on the field and is progressing well. He's expected to start a minor league rehab assignment next week. ... RHP Ben Heller will be shut down for a week with a small flexor strain in his right arm.
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