"It's not really anything I'm focused on," Johnson said of the record. "It's great, but our ultimate goal is our team record at the end of the year and going further than that. Personal achievements are always second."
The Orioles (22-14) have won five of their last six and are now 3-2 in extra-inning games after going 16-2 in those contests last year.
Tommy Hunter (3-1) picked up the win with 2 1/3 perfect innings of relief, extending his scoreless innings streak to 14 2/3.
For five innings, Minnesota right-hander Mike Pelfrey held the Orioles scoreless, allowing just five hits and a walk, before tiring quickly.
Nick Markakis led off the sixth against Pelfrey with a double. Two batters later, Chris Davis doubled him home. J.J. Hardy doubled to score Davis and then Chris Dickerson doubled to plate Hardy.
It was the first time since Aug. 26, 2011 that the Orioles had doubled four times in one inning and the first time since Aug. 30, 2012 that they had at least four extra-base hits in a single frame.
The Orioles' doubling trend continued in the seventh against reliever Josh Roenicke, the son of former Orioles outfielder Gary Roenicke.
Nate McLouth doubled to lead off the inning and scored on an RBI single from Markakis. Davis later added another RBI double to tie the score at 6-6.