Arroyo (3-4) logged his first victory since April 15, scattering five hits while walking one. The right-hander struck out five.
Lutz, called up from Class AA Pensacola last month to replace the injured Chris Heisey, bashed a three-run homer in the second inning, giving the Reds all the momentum they would need in completing a three-game sweep of the Brewers.
Xavier Paul also went deep in the victory.
Brewers starter Wily Peralta (3-3) was touched for four runs (three earned) in five hits over six full innings.
Jean Segura and Yuniesky Betancourt each supplied two hits for reeling Milwaukee, which fell for the ninth time in 10 games.