In the top of the second, though, Baltimore's designated hitter did something about it.
He hit a go-ahead grand slam in a seven-run inning and Baltimore beat the New York Yankees 11-5 on Tuesday night.
"It felt like the first inning would never end," Davis said. "And then we were able to come out there and take back the momentum and really quiet the crowd."
Nick Markakis had a two-run homer among his three hits for the Orioles, who have won four of their last six, but finished July 13-14, their first month below .500 all season. They'll start August 5½ games behind the Yankees for the AL East lead and right in the thick of the hunt for the two wild-card spots.
Tillman said that on Monday, he thought he would be too sick to pitch, but he started a course of antibiotics and felt better on Tuesday morning.
"I didn't feel all that good," Tillman said. "There's no excuse to not make pitches early on."
Orioles manager Buck Showalter said he was close to bringing in a reliever for Tillman. But once he made it out of the first, he talked to pitching coach Rick Adair, and made some adjustments and relied on catcher Matt Wieters.
"Sometimes you have some outings where you are just not carrying everything you need to, your velocity is down a little bit," Showalter said. "Rick just gave him a different wrinkle and a different toy to play with and Matt getting him through those last four innings was pretty special to watch."
Tillman (4-1) was charged with four earned runs and allowed eight hits with three strikeouts in his five innings.
Ivan Nova allowed a career-high nine runs in five innings for New York, which tied a season-worst skid with four straight losses and made some dubious history in the process. According to STATS, LLC, the Yankees haven't led by five or more after the first inning and then trailed after the second since at least 1918. The Yankees have lost nine of 12.
Nova (10-5) struck out five, allowed 10 hits and lost in consecutive starts for the first time in his career. He has one win in his last seven starts, and the Yankees are 14-7 in his games.
"That's something he has been really good at this year: not letting things unravel," Yankees manager Joe Girardi said. "And tonight it did, for whatever reason."
The Yankees teed off on Tillman in the first. He didn't get an out until he fielded Nick Swisher's groundball and threw to second for a force, after allowing an RBI single by Curtis Granderson and Robinson Cano's two-run homer. He later committed an error on Ichiro Suzuki's RBI grounder that made it 4-0. Russell Martin added a run with a single before he got caught in a rundown between first and second. Ramiro Pena finally grounded out to end the inning.
The last time New York led by at least five after one inning and then lost was May 4, 2007, against Seattle, when the Yankees blew a 5-0 lead and lost 15-11.
By the time Tillman made it back out to the mound, he had a two-run lead thanks to Davis' homer, Mark Reynolds' double and Omar Quintanilla's two-run single -- all the runs coming with two outs. He settled down to pitch four shutout innings to hang onto the lead and win his third straight decision.
"It's not easy to go out there and give up a lot of runs to this offense in this ballpark and then stay in there and shut the door after that, so I'm proud of him for doing it," Davis said.
Wilson Betemit helped out by tacking on an RBI double in the third and a single in the fifth.
It was the first grand slam of Davis' career. ... Orioles OF Lew Ford doubled in the third, for his first big league hit since 2007. The 35-year-old Ford batted .272 with 32 homers from 2003-07 with Minnesota. He played in Japan, Mexico and the independent Atlantic League before the Orioles signed him to a minor league contract in May. ... No major league team has taken a 5-0 lead and given it up that quickly since Washington was up 5-0 after the first inning against the Marlins on July 6, 2006, then trailed 7-5 after two. ... The last time the Yankees led 5-0 after one inning and lost by six runs or more was Aug. 6, 1991, at Chicago. ... Before the game, the Yankees obtained third baseman Casey McGehee from Pittsburgh for reliever Chad Qualls, giving them a right-handed batter to plug in while Alex Rodriguez and Mark Teixeira recuperate from hand injuries. ... Yankees RHP Phil Hughes is set to start Wednesday afternoon against Baltimore lefty Zach Britton. ... Jeter doubled in the first inning, making him 39 for 97 (.402) when leading off a game.