Twins reliever Matt Guerrier (1-2) surrendered a one-out walk to Gregor Blanco and Martin Prado sent him to third with a single. Jose Mijares came in to pitch, and Braves Manager Bobby Cox put the runners in motion with Blanco charging down the line from third.
Conrad squared around and put down a bunt to the left of the mound and Mijares had no chance to stop Blanco from crossing the plate with the go-ahead run.
Billy Wagner made the lead hold up, collecting his 11th save to help the Braves even their three-game inter-league series with Minnesota at 1-1.
Atlanta starter Derek Lowe tossed 7 1/3 innings, allowing two runs on six hits. Jonny Venters (2-0) picked up the win after getting the last out of the eighth inning.
Twins starter Nick Blackburn pitched well, surrendering two runs on six hits over seven innings of work.
Swim Week Miami Beach 2014 [PHOTOS]