Eight players had held at least a share of the lead during the day, but it was the 26-year-old Schwartzel who turned in one of the great finishing performances in major championship history.
Schwartzel's final putt from 20 feet curled into the side of the cup for a 6-under 66, the best closing round at the Masters in 22 years. He finished at 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 two strokes back at 276.
"Just an exciting day," Schwartzel said. "So many roars, and that atmosphere out there was just incredible. A phenomenal day."
Tiger Woods was in a group at 278, failing to capitalize after making four birdies and an eagle to shoot a 31 on the front side. He missed short putts at both the 12th and 15th holes, limping to the finish with a 36 on the back nine.
"It could have been," he said. "I hit it good all day."
Rory McIlroy, who entered the day with a four-stroke lead, suffered a stunning collapse.
Still leading by one shot as he headed to the back nine, the Northern Irish golfer hit a tee shot next to the cabins left of the 10th fairway and twice hit a tree to make triple bogey.
He three-putted from 7 feet for bogey on the 11th, four-putted from about 12 feet on the next hole and then buried his head into his forearm as the loss began to settle in.
McIlroy shot 80, the highest final round by the 54-hole leader since Ken Venturi in 1956.
Schwartzel becomes the fourth straight first-time major champion, following Martin Kaymer of Germany (PGA Championship), countryman Louis Oosthuizen (British Open) and Graeme McDowell of Northern Ireland (US Open).
Schwartzel was the first Masters champion to close with four straight birdies. He got up-and-down from behind the 15th green for birdie to briefly take a share of the lead before Scott made a two-footer ahead of him on the par-3 16th.
Schwartzel answered with a 15-foot birdie of his own on the 16th to catch Scott again. Then came the pivotal 17th, where Schwartzel made a 10-foot birdie to hold the lead by himself for the first time all day.
South Africans now have won two of the last three majors, following Oosthuizen winning at St. Andrews last summer. This one came on the 50th anniversary of Gary Player becoming the first international player to win the Masters.
"I am absolutely delighted for Charl and South Africa. Congratulations and very well done to him. That is how you finish like a champion!" Player said on Twitter.
In so many respects, this looked more like 1986 when Jack Nicklaus charged on the back nine to win a sixth green jacket over a Hall of Fame field.
There were twice as many possibilities at this Masters, though, from Woods and former Masters champion Angel Cabrera, from Geoff Ogilvy and Luke Donald, from K.J. Choi and Bo Van Pelt, who made two eagles on the back nine.
