The Brewers produced a seven-run second inning for a six-run lead, but they could not hold it while trying to win three games in a row for the first time in more than a month.
San Diego captured its fourth straight, thanks to a 17-hit attack.
Venable's homer was followed in the fourth by a two-run double from David Eckstein and the Padres closed to within one in the following inning on a solo homer by Kyle Blanks.
San Diego then took the lead with a three-run sixth. Oscar Salazar doubled home the tying run and scored the go-ahead tally on a sacrifice fly by Eckstein.
Only three of the seven Milwaukee runs were earned and Edward Mujica came in to relieve starter Chad Gaudin in the big second inning. Mujica (3-4) stayed around for 4 1/3 innings and got the win thanks to the San Diego comeback.
Tim Dillard (0-1) took the loss after being able to retire only one batter in the sixth.