Jurickson Profar homered and scored twice, while fellow rookie Engel Beltre got two hits in his first big league start. Texas went home leading the AL West after going 5-1 on its swing to St. Louis and Yankee Stadium.
Holland (6-4) threw his sixth career shutout -- it was the lowest-hit shutout by a visiting Rangers pitcher against the Yankees since the Texas franchise moved from Washington for the 1972 season.
Holland did more than give the bullpen a break. He also spared the Rangers a possible inconvenient return to the Bronx -- a huge rainstorm was due later in the afternoon, and Texas isn't scheduled to play in New York again this season.
The 26-year-old lefty struck out struck seven, walked two and didn't permit a runner after the third inning. He was in complete command in a 92-pitch performance, throwing a sharp slider for strikes, and won for the first time in five starts.
Holland began the game at 0-5 with an 8.85 ERA against the Yankees in regular-season play. He had shown a glimmer of success, however, going 1-0 and throwing 5 2/3 shutout innings against them in the 2010 AL championship series.
The Yankees hit a few flyballs that were caught on the warning track, and left fielder David Murphy contributed a sliding grab. Backup catcher Geovany Soto helped, too, throwing out Robinson Cano at second base after Cano drew a leadoff walk in the seventh and tried to advance on a ball in the dirt.
Phil Hughes (3-7) pitched well, yet has won just once in his last eight starts. He allowed five hits in eight innings after getting seven days' rest following a rugged outing last week against the Dodgers.
The 20-year-old Profar, rated among the top prospects in baseball, led off the fifth with his third home run of the season.
Texas also scored following an unusual play in the third. David Murphy opened with a single and took off a full-count pitch as Profar took a checked-swing. Romine, the catcher, made a strong throw to second, Murphy was tagged and wandered off the bag, thinking he was out.
Plate umpire Gerry Davis checked with third base ump Mark Carlson, who ruled that Profar held up his swing and that it was ball four. Murphy was entitled to second on the walk, but was out because he walked off the bag on his own.
Texas manager Ron Washington briefly discussed the call with second base Dan Iassogna, then went back to the dugout.
The Rangers have not scored in the first inning for 19 straight games. ... Yankees OF Brett Gardner got the day off. ... Rangers RHP Joakim Soria (Tommy John surgery) has retired all nine batters he's faced in three minor league rehab assignments. He's moving up to Triple-A Round Rock and is set to pitch on Friday. ... Texas RHP Alexi Ogando (shoulder inflammation) will throw a bullpen session Friday. ... RHP David Phelps (5-4. 4.01) starts for Yankees on Friday night at Baltimore. ... Texas rookie LHP Martin Perez (1-1, 3.65) starts at home on Friday night against Cincinnati RHP Johnny Cueto (4-1, 3.21).