The Brewers erupted for six runs in the first inning, set in motion by pitcher Barry Zito's throwing error.
Aramis Ramirez emptied the bases with a three-run double during the outburst, which also included a two-run double by Brewers starting pitcher Marco Estrada.
But the hurler pulled up lame at second base following the hit and had to be removed.
Milwaukee's bullpen coughed up five runs over the next two innings before Veras (3-1) came in to close the door, striking out three over a pair of shutout frames.
Jonathan Lucroy went 2-for-4 with a two-run homer for the victors.
Zito (3-2) was pounded for eight runs (four earned) on five hits after lasting just three full innings for the Giants.
Hector Sanchez hit a three-run double in the loss.