Braun delivered a two-run blast and Betancourt added a three-run shot in the initial frame, handing the Brewers a quick 5-0 lead.
Braun later supplied an RBI single, finishing with three RBI as Milwaukee stayed on a roll in the opener of a three-game road series.
Kyle Lohse (1-1) earned the win, allowing one run on five hits while walking one and striking out four over five innings.
The Brewers hurler came out of the game after dislocating the pinky finger of his non-throwing hand during a collision with the Padres' Jedd Gyorko at first base.
San Diego starter Jason Marquis (1-2) was roughed up for seven runs on four hits over 4 2/3 innings.
Pitcher Anthony Bass drove in the only run for the Padres, who dropped a fourth straight.