Teheran (3-1), making his eighth major-league start, allowed five hits, issued one walk and struck out four in his third straight quality outing.
Cory Gearrin recorded the game's final out for his first career save as National League East-leading Atlanta reeled off its fourth straight victory in the opener of a three-game set.
Dan Uggla sparked the Braves' offense with a three-run homer.
Twins starter Kevin Correia (4-4) was touched for five runs on eight hits over four full frames.
Josh Willingham cracked a solo homer for Minnesota, which dropped a sixth straight.
Swim Week Miami Beach 2014 [PHOTOS]