Tillman (14-2) scattered four hits, walking two and striking out seven as he won his fourth consecutive start, again holding the opponent to exactly one run. Baltimore improved to 10-0 in games that the right-hander has started against the American League East this season.
CC Sabathia was charged with the loss on his 36th birthday. The left-hander retired 15 of 17 through one stretch but allowed four runs and seven hits over 6 2/3 innings, permitting a two-run single to Hardy in the first inning and a two-run double to Schoop in the seventh.
Starlin Castro's second-inning RBI single off Tillman accounted for the only New York run. Zach Britton came on to pitch a scoreless ninth for his 30th save in 30 chances this season.
"Every game right now is crucial," Sabathia said. "It would have been great to get the sweep, but to win three out of four is still big. Hopefully we'll carry that momentum into the weekend."
The victory snapped a four-game losing streak for the Orioles. For a team battling illness and injuries, it was a relief.
"Games like today are huge, not to just roll over and say, 'Oh, we'll get them tomorrow at home," Caleb Joseph said.
MOMENTS THAT MATTERED The great awakening: The Orioles' bats awoke from a series-long slumber, doubling the amount of runs the team scored in the first three games against the Yankees. The scoring didn't come in the form of long balls, the source of much of Baltimore's runs this season. Hardy and Schoop provided all the offense necessary.
Sabathia stays in: With double-barrel action cranking in the bullpen, the Yankees opted to stick with Sabathia to face the top of the order in the seventh, despite back-to-back one-out singles by Joseph and Julio Borbon. Sabathia struck out Nolan Reimold looking on a pitch near the bottom of the strike zone, but Schoop flared his two-base hit out of Carlos Beltran's reach in right to end the birthday boy's afternoon.
"I liked the way CC was still throwing the ball," manager Joe Girardi said. "He got Reimold out. You look at Jonathan Schoop, left-handers have gotten him out a lot more than right-handers this year, and in his career. I thought CC had done a good job."
Tillman time: The Orioles' ace ensured there would be no sweep at Yankee Stadium. A day after Baltimore fell out of first place in the AL East for the first time since June 4, Tillman tossed seven brilliant innings.
"It's impressive, especially when you keep in mind he's been facing these guys for a long time. They know everything he's going to try to do," Orioles manager Buck Showalter said.
WHAT'S NEXT Orioles: Right-hander Dylan Bundy (2-2, 3.70 ERA) leads Baltimore into its series opener against the Indians on Friday at 7:05 p.m. ET at Camden Yards. Bundy, at one point considered the top pitching prospect in baseball, hopes to improve on an inconsistent first career start, when he allowed four earned runs in 3 1/3 innings on July 17 vs. the Rays.
Yankees: Right-hander Masahiro Tanaka (7-2, 3.15) will take the ball to open a three-game weekend series with the Giants on Friday at 7:05 p.m. ET, opposed by left-hander Madison Bumgarner (10-5, 2.12). Tanaka is coming off six sharp innings of one-run ball against the Red Sox, in which he walked one and struck out seven.