Leishman began the final round with a five-shot lead and was seven strokes in front of Englishman Rose, who twice cut the margin to two shots on the back nine.
But Leishman would not be denied, the Australian riding a hot putter to birdie the 15th and 16th holes and put the tournament out of reach.
He also birdied the last to card 67 and finish at 23-under-par 261, a tournament record, for his third victory on the PGA Tour at the age of 33.
"There were a few scars from two weeks ago (and I was determined) to not let that happen again," Leishman said in a greenside interview, referring to his fade at the Dell Technologies Championship outside Boston.
Leishman had led by two shots with nine holes left in that tournament before limping home in 40 to finish third.
"It was satisfying to finish off the way I did today," he said. "I really wanted to prove to myself I can do it again from out in front.
"There was a bit of pressure there towards the end. Rosey made a run at me. Five-shot victory probably doesn’t do the day justice. It was a lot closer than that."
American Rickie Fowler rallied late to shoot 67 and tie Rose (65) for second place on 18-under.
Spieth, the 2015 FedExCup champion, closed with a 65 to finish tied for seventh and remains in pole position ahead of the Tour Championship at East Lake in Atlanta starting Thursday.
The 30 players who qualified for the final event will vie for the $10 million bonus awarded to the winner of the season-long points competition.
The top five control their own fate in Atlanta. Win the tournament and they also win the FedExCup.
Superb medium-length putting clinched the wire-to-wire victory for Leishman as his wife Audrey looked on, two years after she nearly died of toxic shock syndrome.
Now healthy again, she recently gave birth to the couple's third child.
Leishman is no stranger to emphatic victories. He won an event by 11 strokes on the PGA Tour's feeder circuit in 2008, and two years ago beat a world class field by six strokes at the Nedbank Championship in South Africa.
He also lost a three-way playoff won by Zach Johnson at the 2015 British Open at St. Andrews.
(Reporting by Andrew Both in Cary, North Carolina, editing by Gene Cherry / Ian Ransom)
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