Harvey (3-0) didn't allow a hit until Justin Morneau homered off the right-field foul pole with two outs in the seventh inning at a chilly Target Field.
The Pole had two break points in Murray's next service game, but once the Scot survived that test, the momentum was clearly with him and his victory was never in serious doubt.
Danica Patrick, the pole winner two weeks ago at Daytona, struggled with her car from the start, going two laps down by the 60th lap and later getting penalized for a tire violation.