Baltimore produced a big offensive performance to win its fifth straight and climb within a half game of the New York Yankees for the lead in the American League East.
Wieters accounted for at least one run with each of his hits. He had an RBI single during Baltimore's four-run first and then drove in another with a ground-rule double in the third.
The Orioles put together a five-run fourth inning, during which Wieters contributed a two-run single, and he had another RBI double in the sixth.
Tommy Hunter (3-3) picked up the win despite giving up five runs on seven hits in six innings.
Eric Bedard (4-7) was roughed up for seven runs on eight hits in just 3 1/3 innings to take the loss.
The dozen runs were the most the Orioles have scored in a game this year.