The first inning, though, was the only one that mattered.
Davis, a heralded prospect making just the third start of his major league career, loaded the bases with no outs in the first, but the Orioles couldn't get the ball out of the infield and failed to score.
They never had much of a chance after that as Davis retired 25 of the final 28 batters he faced on his way to a shutout that doubled as his first big league win. He allowed three base runners to start the night and three more for the rest of the game.
"You've got to congratulate Davis on a great game," said Orioles manager Dave Trembley, who was ejected in the seventh - his fourth ejection of the season and 10th in his career - for arguing balls and strikes. "Complete games are a rarity these days, and to do it this late in the season and to do it in the big leagues is a tremendous accomplishment."
Davis, 24, became the first starter to earn his initial major league win in a shutout since the Toronto Blue Jays' Scott Richmond did it last September with six scoreless innings against the Orioles in his fifth big league start.
Counting the Boston Red Sox's Clay Buchholz's no-hitter on Sept. 1, 2007, in his second major league start, the Orioles have now allowed a fledgling pitcher to shut them out in three consecutive Septembers.
"He threw a great game, he used all his pitches and he got outs in big situations," said Orioles right fielder Nick Markakis, who struck out on Davis' 124th pitch to secure the shutout. "We let him off the hook easy in the first inning. That's the way it goes."
Before an announced crowd of 12,426, Davis allowed four hits and struck out 10 - tying the Philadelphia Phillies' Cole Hamels for the most against the Orioles this season. In his previous start, Davis gave up eight runs in 2 2/3 innings against Boston.
Instead of winning the four-game series, the Orioles (60-86) split with the Rays (74-73), who had lost 11 straight before coming to Baltimore.
It was the 10th shutout pitched against the Orioles this season and the 16th time in their 38 second-half losses that they have scored two runs or fewer.
"Our best chance was in the first, and we needed to either make a productive out or get a hit," Trembley said. "And we didn't do it."
But Markakis, who entered just 5-for-19 this season with the bases loaded, hit a bouncer to third base for what should have been a double play.
Evan Longoria failed to step on third before throwing home for the forceout. The Orioles, though, couldn't take advantage of the mistake.
The Orioles had a runner in scoring position only once more in the game, when Michael Aubrey doubled with one out in the fifth. While Davis (1-1) was mowing down hitters, the Orioles were warming up pitchers at a frenzied rate.
Entering the night, the Orioles knew they would have to use a committee approach with lefty Mark Hendrickson making his first start since May 12.
Hendrickson, who was 1-4 with a 6.35 ERA in seven starts before being moved to the bullpen and excelling, hadn't pitched more than four innings since May 1.
Hendrickson lasted 3 1/3 innings Thursday, allowing two runs on five hits.
"I had a different kind of energy going out there the first inning; obviously it is a little bit different coming out of the bullpen versus starting," Hendrickson said. "But I slowed myself down, made some pitches and for the most part tried to keep my team in it."
After Hendrickson (5-5) was removed with 57 pitches thrown, the Orioles shuttled in six relievers, who allowed five hits and five walks but a lone run in 5 2/3 innings.
It was all over in the first, though, when Davis pulled off the great escape.
"Anytime you can have an opportunity to get a big inning off a guy, you have to take advantage. Unfortunately we weren't able to get the job done right there," said Aubrey, who had two of the Orioles' four hits. "And that totally changed the momentum and his thought process. You could see he gained confidence after getting out of that inning."