The double gives Wieters 14 hits in his last 36 at-bats on the heels of a 3-for-42 stretch.
Phillies right fielder Hunter Pence nearly had a play on it, but appeared to hit the wall before having a chance to jump and full extend.
"I felt like I was pretty close," Pence said. "I hit the wall as I was jumping so I kind of got stuck. I haven't seen the replay. I don't really want to watch it."
With the win, the Orioles captured their second consecutive series, restoring any faith that might have been shaken after the upstarts endured a 3-11 stretch.
"We went through a tough two-week span," third baseman Steve Tolleson said. "Anytime we can get the momentum going back our way, it's big. Jones did it with the home run last night, Wieters shut it down for us. That's pretty special. You can't do any better with a day off tomorrow."
Baltimore has won nine straight in extra innings, the longest stretch in team history.
Sunday's win and that stretch as a whole would not have been possible without another stellar effort from the Orioles' bullpen, which came through with four scoreless innings on Sunday.
During the three game series, the 'pen gave up only one run in 14 innings.
Darren O'Day -- Sunday's winning pitcher -- and Dana Eveland led the way with three shutout innings, while Luis Ayala, Troy Patton and Jim Johnson each had two. Kevin Gregg also threw a scoreless frame.
"It's because we have multiple people pitching well that we're able to move it around," manager Buck Showalter said. "We're in pretty good shape."
The bullpen's effort came in support of Orioles' starter Jason Hammel, who battled through six innings while sweating through three jerseys, matching a season-high 115 pitches in temperatures exceeding 90 degrees.
"It's a grind," Hammel said. "You've got to find a way to get it done when you don't have your best stuff or you're just not getting things done the way you're used to. That's the difference between teams that win one-run ball games and the teams that kind of just sell out and die after a while."
Hammel allowed four runs on six hits and a season-high five walks -- a product of poor fastball command and a desire to pitch around certain hitters in given situations.
The Phillies did most of their damage in the third, scoring three runs. With two outs and Hector Luna on first, Jimmy Rollins walked and Juan Pierre singled to load the bases. Pence's single narrowly evaded the glove of both Hammel and a diving Robert Andino, plating a pair of runs.
Jim Thome followed with a run-scoring single, poking a fastball through a massive hole Baltimore's defensive shift created on the left side of the infield.
In the fourth, Pierre singled, moved to third on a pair of walks and scored when Hammel threw a wild pitch.
But that would be all the offense Philadelphia mustered against Hammel, as he struck out Carlos Ruiz to strand a pair. Hammel also pitched out of a bases-loaded jam in the first by inducing a popout from Shane Victorino and striking out Ruiz.
Hammel, who has been dealing with a sore right knee for nearly a month, entered the fifth inning having already thrown 88 pitches, but he retired the Phillies in order.
That brought him to 104 pitches and gave Showalter and pitching coach Rick Adair thoughts of pulling him.
"Rick just said, 'Hey Ham,' and I said, 'You're not taking me out, you're not telling me I'm done,'" Hammel said. "I said, 'I want to go back out.'"
Hammel returned to the mound for the sixth, and again retired the side in order.
"A lot of guys after five innings in the heat are up there in the runway with the fan, kind of semi-apologizing and saying, 'I'll get them next time,'" Showalter said. "He said, 'I want another inning.'"
The Orioles opened the scoring in the first, plating a run when Jones, Wieters and Ronny Paulino hit consecutive two-out singles.
With Baltimore down in the fourth, 4-1, the rarely used Tolleson provided the game-tying three-run homer off Phillies left-hander Cliff Lee, who finished with four runs on seven hits and two walks in six innings. Lee took another no-decision to prolong his winless start to the season.
After Mark Reynolds walked and Steve Pearce doubled, Tolleson turned on a cutter that was down and in from Lee and pounded it to the stands in left.
The homer, which also came with two outs, was Tolleson's second of the season and third of his career.
"That was a pretty special moment, but also for the team," Tolleson said. "That was a big spot in the game, because it was tied back up. Then we let Wieters do what he does in the 10th. That was fun."