Desclafani (2-0) held Milwaukee hitless until Adam Lind's double with two outs in the fourth. Hector Gomez's fifth-inning single was the only other hit off Desclafani, who struck out five and ran his scoreless innings streak to 15.
It was the third straight strong outing for Desclafani, acquired by the Reds in a December trade for pitcher Mat Latos. In his previous outing last Tuesday, he held Chicago to two hits and no runs over seven innings.
Desclafani and Milwaukee starter Wily Peralta (0-2) were locked in a scoreless battle through five innings. The Reds got to Peralta in the sixth. Brayan Pena drove in the game's first run with a sacrifice fly and Cozart followed with a three-run homer.
Votto added a two-run homer in the seventh off Peralta, who allowed six runs and eight hits over seven innings.
It marked the second consecutive rough start for Peralta, who yielded four runs and 10 hits against St. Louis on Wednesday.
Ryan Braun homered with one out in the ninth for the Brewers.
Cincinnati appeared to score in the second when Pena slid into home and was ruled safe on Desclafani's single. Umpires overturned the call after a Milwaukee challenge.
Milwaukee threatened in the fifth. With runners on first and second and one out, Reds catcher Pena made a diving catch of Peralta's popped up bunt attempt. Negron threw to first for an easy double play.
Reds: Catcher Devin Mesoraco remained away from team for an undisclosed family issue. He is expected to return Tuesday, manager Bryan Price said. Mesoraco hasn't played since April 12 due to a left hip impingement. . Desclafini was hit in the foot in the fourth inning but remained in the game.
Brewers: Second baseman Scooter Gennett sat out after receiving five stitches to close a wound to a knuckle on his left hand that he suffered in the shower after Sunday afternoon's game in Pittsburgh. Gennett said he sliced open the knuckle on a metal shower rack. "It was definitely a freakish thing. It started bleeding everywhere." Gennett said he hopes to return to the lineup by Wednesday. Manager Ron Roenicke, however, didn't rule out a DL stint for Gennett. . Catcher Jonathan Lucroy left the game in the seventh after a foul tip hit his left foot.
Reds: Jason Marquis (0-1, 6.30) takes the mound in the second of the three-game set on Tuesday. The veteran hurler will make his 22nd career start against the Brewers. He's 6-12 against Milwaukee.
Brewers: Mike Fiers (0-2, 5.91 ERA) is 1-3 with a 3.08 ERA in six career games (four starts) against the Reds. Fiers took a 3-1 loss in his only start against Cincinnati last season.