The Brewers won their third in a row, producing a dramatic victory after letting a three-run lead slip away.
The Giants' Santiago Casilla (1-1) came on for his second inning of work in the ninth, but gave up a leadoff single to Jonathan Lucroy. Carlos Gomez reached on an infield single one out later and both runners moved up on a throwing error by shortstop Brandon Crawford.
Betancourt drove in two of the Milwaukee runs with a solo blast in the third and a sacrifice fly in the fifth.
The win went to reliever Jim Henderson (2-0), who worked his way around a walk in the ninth.