Karns struck out two as the Orioles continued their offensive woes.
Baltimore, which fell to 3-10 and have lost eight of nine, didn't get a hit until Rey Navarro's leadoff single in the sixth. Steve Pearce homered in the seventh.
Brian Matusz, who normally relieves, got a start and pitched three scoreless innings, giving up two hits and striking out three.
Rene Rivera hit a two-run homer for the Rays.