Uggla had a single along with his two solo homers to extend his hitting streak to 23 games, but the rest of the Braves' offense had a tough time in a 5-3 loss to the Washington Nationals.
"He's swinging a hot bat," Braves manager Fredi Gonzalez said. "It seems like we just can't get the big three-run homer or even two-run homer, a crooked number up there to get us back on the board."
Uggla's effort was bested by Washington's Rick Ankiel, who had two home runs off Atlanta starter Jair Jurrjens (12-4). Jurrjens allowed five runs and seven hits in five-plus innings, his first loss in eight starts.
"I was trying to be too perfect," Jurrjens said. "It was a horrible performance today."
Bourn, acquired in a trade with the Houston Astros on Sunday, batted leadoff in his first appearance for the Braves. He picked up his first hit for his new team with a single on the second pitch of the game and finished 1 for 4.
"I know it's going to be a bit different for a little while, but as time goes on, I'll get more used to it," Bourn said.
Uggla, for one, was already pleased with his new teammate.
"After just spending last night and today with him, he's a great fit for this clubhouse," Uggla said. "I think he's going to be huge for this team."
David Ross had a solo homer in the seventh inning for Atlanta, which has lost straight.
Nationals starter Livan Hernandez (6-10) allowed one run and six hits, struck out three, and did not walk a batter in six innings. He also drove in a run as the Nationals won their third straight.
Jayson Werth led off the bottom of the second with a double and advanced to third on a groundout. With two outs, Atlanta intentionally walked No. 8 hitter Wilson Ramos to face Hernandez, who slapped an opposite-field single to give the Nationals a 2-1 lead.
Atlanta loaded the bases with one out in the fourth inning, but Hernandez got out of the jam when Ross grounded into a double play.
"If I get a hit there, we score some more runs, we win the game. A momentum changer. I ground into a double play and it kind of sets the tone back to their side," Ross said. "That home run was meaningless. I'd rather have a big hit than a meaningless home run."
Another double play ended a Braves chance in the fifth. After Alex Gonzalez led off with a single, Hernandez fielded Jurrjen's sacrifice bunt attempt and threw to second to start the double play.
"The whole 'getting them in' part has been kind of tough lately, but that's baseball and it happens," Uggla said. "You've got to grind through it and keep working and keep staying positive and keep getting those runners in scoring position. It's not going to be like that forever. We've got too good a team."
Drew Storen pitched the ninth for his 27th save.
Atlanta's Freddie Freeman extended his hitting streak to 16 games with a fourth-inning single.
Notes: Atlanta placed RHP Scott Linebrink on the 15-day DL (lower back strain). ... Jurrjens was the No. 8 batter in Atlanta's lineup, the first time the Braves' starting pitcher was in the lineup outside of the No. 9 spot since Aug. 12, 1941, according to STATS LLC. ... Washington manager Davey Johnson said RHP Stephen Strasburg, recovering from Tommy John surgery, will likely have a minor league rehab start next week. Nationals GM Mike Rizzo has said Strasburg may be able to return to the Nationals in September, and Johnson suggested Strasburg may replace RHP Jordan Zimmermann in the rotation. Zimmermann had the same surgery in 2009 and the Nationals have said his innings will be limited this season.