It was the third time Bradley has prevented an opponent from hitting a home run this season, and this one helped the Red Sox maintain a three-game lead in the American League East over the Yankees with 11 games to go.
"Yeah, I thought I had a chance," said Bradley. "It was hit really well and I happened to race toward the gap and the fence at the same time. And there's not really much thinking going on, just one of those bang-bang type of plays. Got to go up there and go get it."
"Jackie goes up against the wall, takes it back, and it's a play that we're not surprised by it just because of how many great plays he's made for us," said Red Sox manager John Farrell.
The drive by Davis was belted to right-center, and Bradley turned his body sideways as he made the impressive haul.
"It was one of those ones where I was going the opposite way," said Bradley. "Those type of plays I always like to square back up towards home plate if I can, and that way I feel like I have more body control and am able to get my glove in a certain direction. So I just try to square up and absorb the blow with the big part of my body."
Now the debate is this: Of the three homers Bradley has taken back this season, which play was the most impressive?
Bradley took a walk-off homer away from Ryon Healy on May 19 at Oakland in spectacular fashion, getting his glove hand high up in the air before bringing it back.
Then there was the July 16 gem on Sunday Night Baseball against the Yankees, when Bradley brought Fenway Park to a deafening roar by reaching up over the railing above the Red Sox's bullpen in right-center to rob Aaron Judge.
According to Statcast™, Bradley's theft on Tuesday came on a drive by Davis that had a hit probability of 78 percent and an exit velocity of 101.5 mph.
"Everybody is going to say Fenway one [against Judge]," said Bradley. "They'll say Healy, two; and this one, three. The Judge one was on ESPN and all they were doing was talking about Aaron Judge that day, and he crushed the ball in the deepest part of the ballpark. Just the timing of it, that will be something that people remember."
But which play does Bradley think was the best?
"I don't know," Bradley said. "I don't rank them. That's not my job. My job is just to catch it."
The Orioles had a feeling he might.
"I don't think anybody thought he wasn't going to make a good bid for it. I hate to say it, it almost looks routine in some ways -- for him especially," said Orioles manager Buck Showalter. "He makes a lot of great plays on balls in the park and some that might go out. It's a play that speed allows you to make. He gets there in time."
Ian Browne has covered the Red Sox for MLB.com since 2002. Follow him on Twitter @IanMBrowne and Facebook. This story was not subject to the approval of Major League Baseball or its clubs.