"It's frustrating, but it's baseball," Sabathia said. "You've got to go out and try to keep the game close. He's been pitching well all year, and it's up to me to try to keep the game close and give these guys a chance to win."
The loss dropped the Yankees three games behind the Rays for the second American League Wild Card spot. Tampa Bay was idle on Monday, allowing the Orioles to climb to within 1 1/2 games in the Wild Card standings.
The pressure of September play bubbled over after the first inning, as both dugouts emptied briefly when Yankees manager Joe Girardi and Orioles manager Buck Showalter were involved in a fiery on-field confrontation.
Showalter said that Girardi had accused third-base coach Bobby Dickerson and the Orioles of stealing signs. In response, Showalter angrily yelled at Girardi and had to be restrained by home-plate umpire Ed Hickox. Both benches were warned.
"[Girardi said,] 'I know what you're doing,'" Dickerson said. "Yelling it, body language, pointing at me. That's it. And I'm a grown man, that's all. I don't see why he was yelling at me. I just said, 'You don't know anything. You don't even know me to be yelling at me.'"
Girardi refused to acknowledge that the incident had been about sign stealing, remaining vague about what had sparked the situation.
"The one thing that I've done the whole time I'm here and everywhere I've been is, I'm going to protect our players at all lengths," Girardi said. "That's what I'm going to do. There was something that I saw and I'm going to leave it at that."
Yankees catcher Austin Romine said that he was too involved in the game to know why Girardi and Showalter were arguing, but added that he asked someone on the Yankees' bench if his signs had been visible.
"I mean, everybody's trying to steal signs," Romine said. "I wouldn't be surprised if they were, but I really don't know what was going on. No one even said anything to me."
Alex Rodriguez and Lyle Overbay hit solo homers for the Yankees, who have lost four of their last five games.
Batting second in New York's lineup for the first time since 2006, Rodriguez hit career homer No. 652 in the first inning, leaving him eight shy of tying Willie Mays on the all-time list. Overbay cleared the wall with a solo blast to open the eighth.
That accounted for the scoring off the dominant Tillman, who tied a career high with nine strikeouts while scattering just four hits.
"His changeup was outstanding tonight," Girardi said. "He also has a good curveball, but I thought his changeup was the equalizer tonight; moving his fastball up and down as much as in and out."
Sabathia (13-12) had won four of his last five starts coming into the outing and limited the Birds to Adam Jones' first-inning sacrifice fly through the first four frames, but finished allowing four runs (three earned) on seven hits over 7 1/3 innings.
"If we'd been scoring runs the way we were the last week, he gets a win tonight," Girardi said of Sabathia, who walked two (one intentionally) and struck out six.
Baltimore pushed ahead in the fifth with small ball, as J.J. Hardy opened the inning with a double, advanced on a groundout and scored on a Matt Wieters sacrifice fly. Nick Markakis singled home Alexi Casilla to give the Orioles a 3-1 lead.
"It's that time of the year, and situations call for it," Sabathia said. "You're trying to get the runner over to third; get runs however you can. So they did a good job of that."
A Sabathia throwing error on Casilla's tapper back to the mound helped set up Baltimore's fourth run, in the seventh, as Sabathia threw high to the third-base side of second, failing to record a forceout.
After Sabathia induced a double-play grounder, Manny Machado then doubled off the high scoreboard in right field, sending Wieters trotting home.
"Giving up that run after getting the two outs was tough," Sabathia said.
Tommy Hunter relieved Tillman in the eighth and struck out the side. Jim Johnson recovered from Rodriguez's leadoff single in the ninth to record his American League-leading 43rd save.
"We're still in it," Romine said. "It's baseball. Anything can happen. We're coming out here to win every game, and you can't count us out. We keep battling and battling and battling."