Valverde gave up four runs in the ninth to blow a save opportunity for just the second time since joining the Tigers a month deep in the season.
The Orioles won their third in a row and handed Detroit its fourth straight loss, equaling the Tigers' longest skid of the season.
Valverde (0-1) came on to protect a two-run lead after Detroit starter Max Scherzer had given up three earned runs on three hits and struck out 10 over eight innings.
Valverde then gave himself a chance to escape the jam when he got Matt Wieters and J.J. Hardy on infield pop-ups.
That brought up Dickerson, who launched a 2-1 pitch to right for his fourth home run of the season.
Miguel Cabrera hit a two-run homer for the Tigers in the first, the Orioles came back to take a 3-2 lead and Detroit then scored single runs in the fourth, fifth and sixth innings -- two of them driven in by Avasail Garcia.
Dickerson's homer made a winner out of Darren O'Day (3-0), who retired the only batter he faced in the top of the ninth.