Volquez, who brought a 6.39 earned run average into the game, allowed five hits without a walk and struck out three. He left the game with a 2-0 lead, after which Luke Gregerson walked a batter during a scoreless eighth.
Martin Maldonado then brought an unusual end to the game by being called out when he was struck by a batted ball in fair territory.
Marco Estrada (2-1) was the hard-luck loser, giving up a lone earned run on five hits in 6 1/3 innings.
Milwaukee had not lost since dropping an 8-2 decision in St. Louis April 13. The Brewers winning streak came after they opened the season with a 2-8 record.