Chamberlain (1-0), the 41st overall selection in the 2006 draft, scattered four hits and a walk. The 21-year-old right-hander pitched out of a jam in the opening frame, fanning two batters to strand runners at second and third.
"To be under pressure in the first inning kind of set the tone for me to know that I would be all right," said Chamberlain, who was promoted from Double-A Trenton on Tuesday. "(Pitching at the Triple-A level) didn't feel any different, and that was a little surprising coming in."
The University of Nebraska product started the season in the Florida State League, where he was 4-0 with a 2.03 ERA and 51 strikeouts in seven starts. At Trenton, he went 4-2 with a 3.43 ERA and 64 strikeouts in seven starts.
Jim Brower gave up two hits over two scoreless frames to notch his 20th save.
Angel Chavez smacked a two-run double in the fifth and Eric Duncan reached base four times with a double and three walks for the Yankees (58-43), who've won 12 of their last 14 games.
Jay Bruce belted a three-run homer, his fourth, in the sixth for the Bats (50-53), who've dropped 11 of 13. Jesse Gutierrez, Joey Votto and Aaron Herr collected two hits apiece.
Louisville starter Richie Gardner (2-4) yielded four runs on nine hits and two walks with one strikeout in five frames.