Pettersson ended at 12-under-par 276 for a two-shot victory over Brett Wetterich and Zach Johnson. He played the final three holes of his third round in the morning -- highlighted by a 45-foot birdie putt at the 17th -- and was even-par over 21 holes Sunday.
The win at Jack Nicklaus' tournament was not only good for a spot in the next two majors, it also netted Pettersson a career-best check of $1.035 million. He won $954,000 for his first win at last October's Chrysler Championship.
'This is a dream come true to even play in this tournament,' Pettersson said. 'And to win -- it's just phenomenal.'
Wetterich fired a five-under 67 in his final round, while Johnson shot a two- under 70 to reach 10-under-par 278.
Phil Mickelson made some of the most spectacular shots over the last two days of the tournament, but finished in a tie for fourth place at nine-under-par 279. Mickelson, who was playing in his first Memorial since 2002, shot his third straight 70 in the final round.
'It's been a more draining week than normal because of the delays...but a lot of fun, all in all,' said Mickelson.
Brandt Jobe fired a 67 and Adam Scott shot a 69 to finish tied with Mickelson at Muirfield Village.
Pettersson was at 11-under for a two-shot lead heading into the final round.
Weather wreaked havoc on each of the first three days, but the final round experienced only a brief delay of around 30 minutes in the afternoon.
Mere seconds before the horns sounded for the suspension, Pettersson beat the heavy rain with a chip-in birdie from behind the green at the par-five 11th.
That shot -- Pettersson's third birdie of the day -- restored a three-shot lead he had squandered with a bogey from a bunker at the 10th.
Pettersson found trouble at the par-four 13th, but saved par from a bunker with an eight-foot putt.
'Every time I hit it bad, I followed it up with a good one, which was nice to get back into it,' Pettersson said.
With his lead down to two shots heading to the 15th hole, Pettersson found the rough with his approach, flopped a shot within 14 feet and made a right-to- left birdie putt to go ahead by three again.
Pettersson slipped to his third bogey of the round at the 18th, but it didn't matter. After making the putt, he celebrated with a simple pump of his long putter and was greeted by Nicklaus as he walked off the green.
One of the keys to Pettersson's success this week was his ability to escape the tournament's furrowed bunkers.
Entering the Memorial he was ranked 107th on tour with a 47.9 sand-save percentage. Over his last four rounds, however, he was 7-for-9 out of the bunkers -- good for fourth-best in the field.
Asked if he thought the experimental bunkers were overrated, Pettersson balked.
'I don't know about that,' he answered. 'Somehow I got lucky.'
Not only did he sneak into the top-50 in the world rankings on the final day such a standing would count for the British Open, Pettersson also managed to escape the chore of attempting to qualify for the U.S. Open on Monday.
'That's nice. I wasn't thinking about that at all,' Pettersson claimed. 'I was just trying to get the job done on the back nine.'
Vaughn Taylor, Trevor Immelman and Woody Austin tied for seventh place at eight-under-par 280. Paul Azinger finished alone in 10th at minus-seven, while Jose Maria Olazabal ended one shot further back in 11th.