"We were in it 'til the last out," said Arrieta, who gave up seven runs in a season-low 3 2/3 innings to take the loss. "The guys really battled and did what they could to come back."
The O's faced deficits every step of the way on Sunday, but managed to fight back at every turn.
Down 7-1 in the sixth, Nick Markakis hit an RBI double and Wieters followed with a two-run home run.
That momentum carried into the seventh, when Markakis hit another double, this time driving in two to trim the Rays lead to just one, 7-6.
"I don't think it surprises anybody, especially me," manager Buck Showalter said. "There's a good air about the dugout from the first inning on. It's been that way since Opening Day. They feel like, as a group, they can overcome some things.
"Our guys tried to overcome it today and came real close to doing it."
The Orioles bullpen retired 30 of the first 31 batters it faced in the series, including 10 of the first 11 on Sunday, keeping the game within reach.
But that streak ended in the eighth, when Elliot Johnson and Ben Zobrist hit back-to-back home runs off of Troy Patton to extend the lead to 9-6.
Still, the Orioles weren't done.
"After I gave up two homers they keep fighting and they keep battling until the game is over," said Patton, who saw the offense score five unanswered runs as he worked through scoreless frames in the sixth and seventh. "I feel like when I've been out there they've been competitive in games, coming back in games in which it kind of looks like we're out of it, so it didn't really surprise me. They've been battling back a lot this season to come back and make games close.
"There's no quit in them."
Nick Johnson hit a solo home run in the bottom of the eighth, leaving the Orioles just two runs behind heading into the ninth.
With runners on first and second with two outs, Adam Jones beat out an infield single to third. When Rodriguez's throw got away from Pena, Hardy scored to bring the Orioles within one, setting up the final at-bat from Wieters.
"We had a chance in the ninth and just didn't come through," Wieters said. "It would have been a nice game to win, but at the same time you know this team is going to keep playing hard and we're not out of any game. That's how we feel in this clubhouse.
"This team never gives up."
The O's have become accustomed to late-inning comebacks this season, already notching five wins in games in which they trailed after seven innings.
The Orioles only recorded five such wins all of 2011, when they posted a 5-83 record when trailing after seven.
"We made a run at the end there, and if Pena doesn't catch that ball there, we may possibly win that game," Markakis said. "You can't hang your heads. It's a good game all around."
There is certainly no head-hanging in the Orioles clubhouse. Not so long as the Orioles continue to sit atop the American League East with a 22-13 record.
The O's lead over the Rays has shrunk to just a single game, but the respect they've earned from their opposition is only growing.
"They've always had those good hitters, and now they've got pitching," Tampa starter James Shields said. "Their bullpen is phenomenal this year. And their starting pitching is going deep into the game. That's one of the recipes we've figured out the last couple of years."
The Orioles are now 8-5 during the last 14 days as they enter the final two games of a 15-game gauntlet that includes matchups against the Yankees, Red Sox, Rangers and Rays.
"I'm real proud of them," Showalter said. "I've been proud of them since we went to camp."
The Orioles have eight players on the disabled list and a bullpen still recovering from playing a 13-inning game, 17-inning game and doubleheader in the span of seven days. Those challenges have forced Showalter and executive vice president of baseball operations Dan Duquette to make 23 roster moves since May 4, creating a constant carousel of players in and out of the clubhouse.
But none of that has ever bled into their play on the field.
"We've got some moving parts because of the injuries, and I think we've handled that well mentally," Showalter said. "I'm proud we've been able to withstand some of the challenges that everybody has over the course of a season. We'll get them healthy and maybe find some good things while we're waiting."