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.
Millions of Getty images now available for free via embed tool
Aaron Carter is still in love with Hilary Duff