Gallardo gave up an RBI double to Ryan Howard in the fourth inning, but allowed just three other hits while improving to 12-8.
The Brewers' pitcher also delivered a two-run single that finished off a four-run fourth inning. Braun's homer in the sixth gave Milwaukee a five-run cushion.
Vance Worley (6-8) lasted just 4 1/3 innings to take the loss. He was touched for four runs on seven hits with three walks.
Braun's homer was his 32nd of the season -- tops in the National League.
The Phillies have lost three in a row.