The 31-year-old carded a four-under 67 to finish seven under with Haas, who was one ahead overnight.
He then claimed the play-off with a par for his 15th professional win, but only his second on the PGA Tour.
World number one Jordan Spieth, the defending champion, birdied the last for a 73 and was tied 18th, seven back.
Playing partner Lee McCoy, the 22-year-old amateur who grew up next to the Copperhead course, followed his third-round 66 with four birdies in a 69 and finished fourth to qualify for the Houston Open.
Haas was two shots ahead into the closing stages, but having made par from a greenside bunker at the par-three 15th, he was unable to do so from a similar scenario at the next and was tied with Schwartzel, who birdied three of his final six holes, including a putt from 64 feet at the 13th.
At the first play-off hole, the par-four 18th, Haas put his tee shot with a three wood into the trees on the right and his second into a greenside bunker.
Schwartzel, the 2011 Masters champion, took an iron off the tee and was pin-high in two, before calmly two-putting to secure the title after Haas could not hole for par from 18 feet.

The ADB said that poor air quality had reached such a serious level that it was "jeopardising health and sustainable growth".
The loan is intended to cut the region's coal use, among other pollution issues.
China is the world's biggest polluter.
The loan will target Beijing city and surrounding areas including Hebie and Tianjin. The region is home to more than 100 million people and accounts for 10% of China's gross domestic product, the ADB said.
"Poor air quality has reached such a serious level that it is jeopardising health and sustainable growth in the capital region," said ADB's urban development specialist Satoshi Ishii.
"[Our] assistance will help reduce emissions and strengthen the environment regulatory framework and capacity of environmental monitoring and enforcement.
"Better air quality will benefit the economy and people's health, both in the region and beyond," he added.
The money from the ADB follows the latest World Climate Summit which is concluding in Paris this week.
The bank said in a statement the loan was expected to be accompanied by co-financing from Germany's KfW Development Bank of €150m ($164m; £108.2m).
The agreement follows Beijing's first "red alert" warning over pollution levels earlier this week.
It was issued late on Monday and lasted until Thursday, and was the first time that China had declared a red alert under the system, which was adopted a little over two years ago.
Schools in Beijing were closed, outdoor construction was halted, limits were placed on car use and some factories were ordered to stop operations.
Emissions from coal-powered industries, cars and heating systems, together with dust from construction sites all help create the dangerous smog.
When the red alert was declared, the US Embassy's air pollution monitor in Beijing said the intensity of the tiny particles known as PM 2.5 were at 291 micrograms per cubic metre.
A reading of 25 micrograms per cubic metre is recommended by The World Health Organization as the maximum safe level.
Despite large investments in renewable sources, China still depends on coal for more than 60% of its power.
South African Charl Schwartzel won the Valspar Championship in Palm Harbour, Florida with victory over American Bill Haas at the first play-off hole.
[NEXT_CONCEPT]
China is to receive a $300m (£198m) loan from the Asian Development Bank (ADB) to help it combat dangerous pollution levels in Beijing city and its surrounding area.