With the victory, the Reds snapped a seven-game home losing streak.
Jose Guillen added a solo homer and a two-run single for the Reds, who had lost 12 of 15 overall posted their fifth straight win over Milwaukee. They swept three games at Miller Park heading into the All-Star break to end an eight-game losing streak.
Cincinnati had a 5-0 advantage before Jose Guillen led off the seventh with his 19th homer, and Branyan capped the six-run inning with a one-out, pinch-hit grand slam off Brooks Kieschnick. It was his third career grand slam and first since April 17, 2001.
Acevedo (1-0) struck out six and walked two in his first start since May 19, 2002.