With the win, the Orioles finished Interleague Play with an 11-7 record -- tying the best mark in franchise history -- and can head into Monday's off-day on a high note.
Entering the eighth inning, the Orioles' offense had struggled to get anything going for the seventh consecutive game.
To that point, the O's had mustered only five hits -- including three weak grounders through the left side and a blooper from Robert Andino -- leaving the team with a .167 average and a 1-for-33 mark with runners in scoring position in its past seven games.
But Jones led off the frame with a single through the right side and Wieters -- who nearly got the day off after catching a night game on Saturday -- made all that moot, blasting the go-ahead homer against Sean Burnett.
Burnett entered with a 1.04 ERA and had allowed only one home run in 26 innings before Sunday.
"Clutch," J.J. Hardy said. "To win a ballgame like that the way we've been swinging was something we needed. It just didn't seem like we were going to piece together a bunch of hits. With Jones leading off that inning and Wiets doing that, it was clutch."
Jake Arrieta's six strong innings and three scoreless frames from the bullpen made Wieters' pivotal blast stand up.
Arrieta turned in his third consecutive solid outing, holding the Nationals to one run on five hits in six innings.
Since being demoted to the bullpen after his June 8 start, Arrieta -- who was put back in the rotation before appearing out of the 'pen -- has given up only six runs in 20 innings, with most of the damage coming on a grand slam from the Mets' Ike Davis.
With help from pitching coach Rick Adair, Arrieta has changed his approach, simplifying things so that all he has to do is go out and execute his pitches.
"This year, the mental side of the game has affected me the most in my career thus far," Arrieta said. "That's part of the maturation process of pitching at this level, and that's something that you have to go through and battle through."
The Orioles' pitching staff allowed just five runs -- three earned -- to put a lackluster offense in position to take two out of three in a series that brought 133,983 fans to Camden Yards during the three days -- the highest total of the season.
The O's bullpen threw eight scoreless innings in the weekend set, lowering its collective ERA to a Major League-best 2.27.
"That's the reason we were able to win two games," Wieters said. "If our pitching wasn't as good as it was this weekend -- both starters and bullpen -- we wouldn't have had a chance in those games."
"Obviously, they have a great bullpen," Nationals shortstop Ian Desmond said. "Arrieta threw the ball well today, too."
Despite showing spotty control and command in the first three innings, Arrieta avoided making any critical mistakes.
He needed 61 pitches to get through the first three frames but allowed just the single run in the third, when Ryan Zimmerman smashed a single over the outstretched glove of a leaping Hardy at shortstop to score Jhonatan Solano, who led off the inning with a double.
Arrieta found his control and settled in from there, throwing 15 strikes out of 19 pitches to retire the side in order in the fourth and fifth.
The right-hander returned to the mound in the sixth after 80 pitches and gave up a chopper up the middle that a hustling Bryce Harper extended into a double. Arrieta followed with a strikeout of Zimmerman and then intentionally walked Adam LaRoche before striking out Michael Morse and getting Desmond to pop up to escape the jam.
Troy Patton entered in the seventh and recorded five consecutive outs, including three strikeouts.
"Troy Patton very quietly has really started to get my attention as somebody that's developed into a guy who can help us," Orioles manager Buck Showalter said. "He ain't scared. Troy says, 'Here's mine. Let's see what yours is and see how it works out.' He's starting to really trust himself."
After Pedro Strop got the final out in the eighth, closer Jim Johnson came on in the ninth and notched his 22nd save.
Fittingly, it was Wieters who recorded the final out, gunning down Desmond on a steal attempt on the same pitch Johnson struck out Danny Espinosa.
For a catcher who prides himself on defense, the final play in the field was just as important as the series-winning home run.
"It's right up there, because it won the game," Wieters said. "Any out you can get, especially the 27th out, is huge."