Trailing 3-0 in the eighth, Milwaukee began a late comeback when Rickie Weeks and Norichika Aoki each notched a single against Sean Doolittle to begin the frame.
Jean Segura followed by scorching a pitch down the first-base line and into the corner for a two-run triple.
Ryan Cook came in to pitch and with the infield playing in, Aramis Ramirez sent a broken-bat bloop into center field, chasing home the tying run.
Then with one out in the 10th and Carlos Gomez on first, pinch-hitter Betancourt laced a hit to right-center off Pat Neshek (1-1) and the speedy Gomez came all the around to score the game-winning run.
John Axford (2-3) notched the decision for the Brewers, who evened their three-game interleague series.
Yoenis Cespedes bashed a pair of homers and starter A.J. Griffin hurled seven shutout innings for the Athletics in the loss.
Notable deaths of 2014 [PHOTOS]