The Reds had won two in a row to tighten the National League Central race, but they had no answer for the two key blows by Davis.
He hit his first two-run shot in the sixth to give the Brewers a 3-2 lead only to see Cincinnati tie it in the bottom half of the inning on a solo homer from Brandon Phillips.
Davis came up in the eighth against Alfredo Simon (5-4) after Aramis Ramirez had drawn a leadoff walk and moved to second on a sacrifice by Carlos Gomez. Davis hit the first pitch from Simon over the wall in center for his eighth homer of the year.
Scooter Gennett followed with a solo shot to make it a three-run lead.
Rob Wooten (2-0) collected the win by working a perfect seventh inning in relief. Jim Henderson gave up a two-out single in the ninth on the way to his 20th save.