McCullers (3-1) followed Dallas Keuchel's six scoreless innings from Thursday's series opener by scattering four hits. He struck out seven without a walk and threw 90 pitches.
Brian McCann belted a three-run home run while Carlos Correa and Josh Reddick each had an RBI single as the Astros improved to 25-11, surpassing the best 36-game start in team history set by the 1972 team.
Similar to Keuchel, McCullers did his best work in the fifth and sixth innings.
The right-hander struck out the side after allowing a leadoff double to Aaron Judge in the fifth. He gave up a leadoff single to Brett Gardner in the sixth and worked around a fielding error by third baseman Alex Bregman.
Will Harris pitched a scoreless seventh, which ended after Chase Headley was ejected by plate umpire Adrian Johnson. Headley contended he was hit with a pitch on a bunt attempt that went into foul territory.
New York's Jordan Montgomery (2-2) allowed four runs and eight hits in six innings.
The Yankees tied a season high with their third straight loss. Despite the setback, New York is 20-8 in its last 28 games.
The Astros took a 3-0 lead with one out in the fourth when McCann sent an 0-1 pitch over the right field wall and into the second deck near the foul pole.
Houston upped its lead to 4-0 with two outs in the fifth. George Springer started the inning with a double and scored on Correa's bloop double in front of Judge.
Judge opened the fifth with a double over left fielder Jake Marisnick's head. McCullers then kept Judge at second by striking out Didi Gregorius, Chase Headley and Aaron Hicks.
NOTES: Houston manager A.J. Hinch visited Monument Park for the first time and took a photograph of Mel Stottlemyre's plaque. He said he was planning on sending it to the former Yankee pitcher and pitching coach. Hinch said he got to know Stottlemyre when he worked with his son in the Arizona Diamondbacks' organization. ... New York DH Matt Holliday made his third start at first base. ... Yankees 2B Starlin Castro limped briefly after catching a pop-up by Houston 3B Alex Bregman in the sixth. He stayed in the game and gave manager Joe Girardi a thumbs-up signal. ... The Astros activated RHP David Paulino from the 10-day disabled list and optioned him to Triple-A Fresno.