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.