Trailing 4-2 in the ninth, the Orioles got a lead-off homer from Nolan Reimold and a two-out solo shot from Adam Jones off closer Hector Santiago to tie the score. Baltimore erupted for six runs in the 10th, highlighted by Wieters' bases-loaded shot off Zach Stewart (0-1).
Five of the 10th-inning runs were unearned, following an error by center fielder Alejandro De Aza, who misjudged Mark Reynolds' deep fly ball to lead off the frame.
Wieters finished 3-for-4 with five runs batted in while Chris Davis added three hits and an RBI in the comeback.
Pedro Strop (1-1) earned the win after tossing two scoreless innings.