Third baseman Miguel Sanó and second baseman Jonathan Schoop each homered twice. Schoop drove in four runs and Sanó finished with three RBIs.
C.J. Cron fell a triple shy of the cycle for Minnesota. He homered, hit two singles and added two doubles.
Eddie Rosario, Jorge Polanco, and Max Kepler also homered for the Twins.
"I think it's easy to say that it's pretty amazing," Twins manager Rocco Baldelli told reporters. "You don't see that in baseball pretty often. I know I haven't seen anything like it. Our guys just continually go up there and they don't give at-bats away. They just keep going at it."
Minnesota previously homered April 20 against Baltimore. The Twins hadn't hit eight home runs in a game since 1963 against the Washington Senators, who are now the Texas Rangers.
Minnesota swept Los Angeles in Anaheim for the first time since 1996.
Minnesota moved to 33-16 with the win. The Twins have an eight-game lead over the Cleveland Indians for first place in the AL Central Division.