The White Sox wasted a four-run rally that forged a tie in the seventh inning and eventually saw their five-game winning streak halted.
Frasor (2-2) retired the last two batters in the ninth and stayed in the game in the 10th, getting leadoff man Mark Reynolds on a groundout. Chris Davis then singled to left and Reimold ended it with his seventh home run of the season.
Baltimore had lost three straight games.
The Orioles built a 4-0 lead through five innings thanks in part to solo home runs by J.J. Hardy and Adam Jones, both of whom have 21 for the year.
A two-run single by Juan Pierre completed Chicago's comeback in the seventh.
The win went to Mike Gonzalez (2-2), who worked the top of the 10th and survived a one-out double by A.J. Pierzynski, who had three hits in the game.
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