Parnevik made his move at the 11th, starting a string of three straight birdies with a 12-footer there.
Barwick had earlier made a spectacular start to this day, opening up with three straight birdies.
He started it with a monster 35-footer across the green at the 13th hole, the first of five straight birdies.
He also put together three straight birdies on the back nine.
Tiger Woods made two straight birdies on 16 and 17 to avoid missing his first cut in 128 events.
Another, the first of his five straight birdies, was an 8-foot putt on 13.
Yesterday, she had three straight birdies on the back nine.
But two straight birdies, at the 11th and 12th, put him far enough in front that he could easily play in for the victory.
He put up three straight birdies, at the 10th, 11th and 12th.
And with a 9-iron to the green on the 18th hole, he had an opportunity for a seventh straight birdie.