Holland, who had been 0-5 with an 8.85 earned run average versus New York in his career, gave up a leadoff single to Ichiro Suzuki in the first inning and a two-out base hit to Austin Romine in the third.
After that he walked two batters -- one who whom was caught stealing -- but faced just one over the minimum 18 batters the last six innings. He struck out seven and walked two in improving to 6-4.
Yankees starter Phil Hughes (3-7) retired the first six batters he faced before the Rangers parlayed two singles, a walk and a sacrifice fly by Ian Kinsler to score Jurickson Profar for a 1-0 lead in the third.
Profar added a home run -- his third of the year -- in the fifth for the Rangers' other run.