Teheran (3-1) gave up five hits, one run — Josh Willingham’s homer in the ninth — and one walk. He struck out four, throwing 80 of his 123 pitches for strikes.
Cory Gearrin earned his first career save by retiring pinch-hitter Oswaldo Arcia on a flyout.
Minnesota has lost six straight.
The previous longest career outing for Teheran was seven innings, a mark he reached in a no-decision April 29 against Washington and a May 9 victory at San Francisco.
After rallying in late innings to win three straight from the Los Angeles Dodgers over the weekend, Atlanta jumped on Twins starter Kevin Correia (4-4) early.
In the first, Jason Heyward singled, advanced to third on Justin Upton’s single and scored on Freddie Freeman’s RBI single. One out later, Uggla hit his eighth homer, a three-run shot that made it 4-0.
Juan Francisco led off the fourth with a double, moved to third on Teheran’s sacrifice bunt and scored on Andrelton Simmons’ sacrifice fly RBI for a 5-0 lead.
Correia had his shortest outing in nine starts this season. In four innings, he allowed eight hits, five runs and one walk.
Correia had no strikeouts for the first time this year and the first time as a starter since April 29, 2012, when he and the Pittsburgh Pirates lost at Turner Field.
Ryan Pressly pitched the fifth and sixth for Minnesota, allowing one walk and striking out one. Caleb Thielbar, recalled from Triple-A Rochester earlier in the day, worked the seventh and eighth, giving up a single and striking out three.
Teheran allowed a single to Justin Morneau in the first, faced the minimum in the second and gave up a leadoff single to Aaron Hicks in the third.
Morneau singled to begin the fourth and moved to second on Trevor Plouffe’s walk, but Teheran ended the threat on Chris Parmelee’s flyout and Pedro Florimon’s flyout.
Teheran, a 22-year-old in his first full season, held Minnesota to just one base runner — Willingham, who was hit by a pitch in the sixth — over the next four innings.
In his past five starts, the 22-year-old right-hander is 3-1 with a 2.41 ERA with two homers allowed. He gave up a combined four homers over his first three starts.
Teheran retired Morneau on a flyout to begin the ninth, but Willingham hit his sixth homer and Plouffe singled to end the pitcher’s night.
Luis Avilan faced the next two batters. Parmelee singled and pinch-hitter Ryan Doumit flew out before Gearrin retired Arcia.