The 28-year-old Australian finished on 15 under par, with American Kevin Chappell his closest rival on 11 under.
Day, whose halfway total of 129 was a record for the Florida event, shot a one-under closing round of 71.
Northern Ireland's Graeme McDowell and Rory McIlroy finished at eight and seven under respectively, while England's Justin Rose was five under.
American Justin Thomas bettered his third-round 75 by 10 shots on Sunday to finish on 10 under in a tie for third. Rose also shot one of the day's best rounds, but his 66 was only good enough to move him into a tie for 19th.
Day dropped two shots on the front nine, but birdied the 10th and 12th to get back to level par for the round.
The US PGA winner also birdied the 16th after a superb chip to the green as he earned his 10th PGA Tour title.
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The miracle involved the healing of a Brazilian man with several brain tumours in 2008, the Vatican said.
Mother Teresa died in 1997 and was beatified - the first step towards sainthood - in 2003.
She won the Nobel Peace Prize for her work with the poor in the slums of Indian city of Kolkata (Calcutta).
"The Holy Father has authorised the Congregation for the Causes of Saints to proclaim the decree concerning the miracle attributed to the intercession of blessed Mother Teresa," the Vatican said on Friday.
She is expected to be canonised in Rome in September.
Beatification by the Catholic Church requires one miracle, while the process of becoming recognised as a saint requires proof of at least two miracles.
Mother Teresa was beatified in 2003 after Pope John Paul II accepted as authentic a miracle attributed to her.
He judged that the curing of an Indian woman suffering from an abdominal tumour was the result of the supernatural intervention of the late Mother Teresa - a claim challenged by Indian rationalists.
There are few details about the recovery of the Brazilian man, whose life the Vatican says was saved in the second miracle.
His identity has not been disclosed to maintain the discretion needed for the investigation, the Catholic New Agency has said.
It says he was unexpectedly cured from brain tumours in 2008 after his priest prayed for Mother Teresa's intervention with God.
Born Agnes Gonxhe Bojaxhiu in Skopje, Macedonia, in 1910, she founded the Missionaries of Charity in 1949, dedicating her life to caring for impoverished and sick people in Kolkata.
Known as the "saint of the gutter", she earned worldwide acclaim for her efforts.
Her critics, however, accused her of mixing with dictators and peddling a hardline Catholicism.

The Niagara County Legislature voted in favour of asking New York's attorney general to investigate on Thursday.
The local water authority said the colour was caused by residue from black carbon filters used to clean the water.
The water authority says July's treatment process was necessary and the discharge within "permitted limits".
An inky and foul-smelling cloud of water appeared at the base of Niagara Falls on 29 July 2017.
Some initially suspected an oil spill, but the Niagara Falls Water Board (NFWB) said it was caused by a "routine" water treatment and apologised for causing alarm to residents and tourists.
In a statement the board said the "inky water" was the result of a "necessary and short term change in the waste water treatment process" at its plant near the city of Buffalo.
Officials say the plant had the correct paperwork to release the discharge - which came from one of its five sediment filtration basins and was being flushed out over the weekend in preparation for contractors to begin upgrade work.
World number one Jason Day maintained his four-stroke advantage to win the Players Championship at Sawgrass.
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Pope Francis has recognised a second miracle attributed to Mother Teresa, clearing the way for the Roman Catholic nun to be made a saint next year.
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The discharge of black smelly wastewater at the base of Niagara Falls has prompted calls for a criminal inquiry.