Millar hit a two-run homer in the second inning and finished with two hits and three RBI. Bako hit a three-run blast in the fourth.
Nick Markakis had three hits for the Orioles -- who came to town winless after being swept at Minnesota in a season-opening three-game series, but won two of three at Yankee Stadium.
Winner Erik Bedard (1-1) gave up three earned runs and five hits in seven innings, with no walks and five strikeouts.
Chris Ray earned his second save of the season.
Alex Rodriguez, who hit a walk-off grand slam homer off Ray Saturday afternoon, hit a two-run shot in the first for the Yankees.
Loser Darrell Rasner (0-1) yielded five earned runs and eight hits in 4 1/3 innings.