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.
Millions of Getty images now available for free via embed tool
Aaron Carter is still in love with Hilary Duff