Baltimore took five of six from the Central Division leaders this season. The Orioles won two of three in the series after sweeping the Twins last week at Camden Yards.
Since July 1996, the Orioles are 42-12 against the Twins.
Minnesota lost a series at home for the first time since dropping two of three to Atlanta from June 10-12. The Twins lost their first series at home to an American League club since they were swept by the New York Yankees from May 10-12.
Jason Johnson (4-9) earned the win, allowing one run and six hits in seven innings with a walk and five strikeouts.
Lohse (10-6) yielded two runs and just four hits over seven-plus innings. He was lifted after giving up the homer to Mora.
Buddy Groom tossed 1 1/3 scoreless innings before Jorge Julio recorded the final two outs for his 25th save.
Chris Singleton gave the Orioles the lead with a solo homer in the top of the first. The Twins tied it in the fifth on Torii Hunter's double and Dustan Mohr's RBI single.