New York (76-67), fourth in the AL East, salvaged the finale of its four-game set against first-place Boston on Sunday when Ichiro Suzuki scored on a wild pitch with two outs in the ninth inning for a 4-3 win.
"We needed it, because we've had some pretty tough games the last couple days," said manager Joe Girardi, whose team could be without Derek Jeter for this series because of soreness in his surgically repaired left ankle.
While they trail the Red Sox by 10 games in the division, the Yankees are 2 1/2 games back of Tampa Bay - with Baltimore (76-66) and Cleveland in between - for the AL's final wild-card spot.
Now New York has a chance to slide past the Orioles with Sabathia (13-11, 4.86 ERA) on the mound in the opener of a 10-game road trip. The Yankees, however, have dropped five straight in Baltimore, their longest skid since losing nine in a row there between 1981-82.
Sabathia hasn't been sharp with a 6.88 ERA since July 21, but he's been helped by 30 runs of support in winning four of five starts. He showed improvement in his most recent outing Wednesday, when he yielded three runs and five hits over 7 1-3 innings in a 6-5 win over the White Sox.
"I feel like I'm getting better," Sabathia told the league's official website. "Like I've said, I'll keep building, keep working and try to help the team win."
The left-hander hasn't fared well in Baltimore lately, though. He's 0-3 with a 5.97 ERA in his five outings at Camden Yards over the past two seasons.
Teammate Chris Davis, who leads the majors with 48 home runs, is 4 for 12 with a homer when facing Sabathia this season. The slugger is 9 for 21 with five homers and nine RBIs in six home games against the Yankees.
After taking three of four from the White Sox to open its homestand, Baltimore looks for its fifth win in six home contests by giving the ball to Tillman (15-5, 3.71).
The right-hander hopes to bounce back after allowing a season-high five walks and four runs over 5 1-3 innings in a 4-3 loss at Cleveland on Tuesday.
"As a starter, your goal is to keep it close and see what happens," said Tillman, who had a 2.57 ERA over his previous five starts. "I didn't do that. I've got to be better.''
Tillman hasn't been at his best against the Yankees, either, going 3-4 with a 7.43 ERA in nine career starts. He gave up five runs and 10 hits over 5 1-3 innings in a 5-4 loss at Yankee Stadium on July 6.
Suzuki, however, is 2 for 16 in this matchup and 3 for 19 at Camden Yards this season.