Robinson Cano's double in the first drove in Suzuki, whose pirouette around catcher Matt Wieters earned style points in addition to a run.
Jeter pulled the Yankees within a run with an RBI single in the seventh against Wei-Yin Chen. But the captain also was part of New York's struggles at the plate with runners in scoring position, a problem all season.
New York loaded the bases with one out in the fourth against Wei-Yin Chen, but Eduardo Nunez popped out and Jeter grounded into a forceout.
"He was putting the ball where he wants," Cano said. "You've got to give them credit. There was nothing we could do."
With runners at second and third and two outs in the seventh, Nick Swisher flied out against Brian Matusz, dropping to 1 for 33 (.030) with runners in scoring position in postseason play.
And a night after scoring five runs in the ninth against All-Star reliever Jim Johnson to win 7-2, the Yankees saw just 12 pitches in a 1-2-3 ninth against Baltimore's closer. Alex Rodriguez, 1 for 9 with five strikeouts in the series, fanned for the final out.
These teams have split 20 games this year. During the regular season, the Orioles took two of three in all three series at Yankee Stadium.
"It's nothing to go crazy about," Martin said. "I feel like we're a good team and we're going to bounce back, and we're going to give them a hard time back home."
Last year, the Yankees won their first-round opener against Detroit but were knocked out in five games. In 2010, they beat Texas in Game 1 of the AL championship series but lost in six.
Not the type of history New York wants to repeat.