The 26-year-old South African closed with four straight birdies, making a 20-footer at the final hole to wrap up a 6-under 66. He finished 14-under 274, enough to deny Australia its first green jacket.
Scott shot a 67 and Day finished with two straight birdies for a 68, leaving both Aussies at 276. It wasn't enough to hold off Schwartzel, who gives South Africa another major champion.
Tiger Woods was in a group at 278, failing to capitalize after shooting 31 on the front side. The 54-hole leader, Rory McIlroy, fell apart on the final day.