Evan Gattis hit a pinch-hit, game-tying home run off Glen Perkins with two outs in the bottom of the ninth to tie the game, 4-4, and Freddie Freeman blooped the game-winning single to center in the tenth to lift the Braves over the Twins, 5-4.
That's seven straight losses for the Twins, who are quickly falling deeper into the American League central basement.
Atlanta struck for two runs in the first inning on a double by Freeman and a single from Brian McCann.
The Twins got one back in the second inning on an RBI single from Pedro Florimon, and then the rain came.
Where the Twins go the precipitation follows. The game was delayed one hour and 16 minutes thanks to the rain, and when the game resumed Mike Pelfrey didn't.
Pelfrey allowed the two runs in the first inning, and ended his night prematurely after throwing just 38 pitches.
Justin Morneau's RBI single following the delay tied the game at 2-2 in the third inning.
The game remained tied until Brian McCann got ahold of an Anthony Swarzak pitch and drilled it over the right field wall for a 3-2 Braves lead. Other than that, Swarzak was fantastic, allowing just three hits over four innings in relief.
RBI singles in the eighth from Trevor Plouffe and Ryan Doumit put Minnesota back on top, 4-3.
Notes: Plouffe left the game in the top of the tenth after taking a knee to the head while sliding into second base. Minnesota Wild forward Zenon Konopka wasn't at the game, but he was in Atlanta and ran into boxing great Evander Holyfield at the airport.