After a final round 1-under 71, the native of Sweden finished 12-under 276. Brett Wetterich (67) and Zach Johnson (70) tied for second at 10-under 278.
It was Petterson's second PGA Tour victory, guaranteeing him a spot in this year's U.S. and British Opens.
"This is a dream come true to even play in this tournament," Pettersson said. "And to win -- it's just phenomenal."
His final round was highlighted by a 45-foot birdie putt at the 17th hole.
Pettersson was even-par over 21 holes Sunday and earned a career-best check of $1.035 million.
Mickelson was playing in his first Memorial since 2002.
Tiger Woods missed the tournament for the first time in nearly a decade.