Sir Winston came on strong late, moving from the rail to the outside down the stretch to overtake pace-setter Joevia and finish in a relatively slow two minutes, 28.30 seconds.
While making his move, Sir Winston appeared to cut off Preakness Stakes winner War of Will, initially raising the prospect of a challenge similar to one that disqualified Maximum Security after it crossed the line first at this year's Kentucky Derby.
Both Sir Winston and War of Will, however, are trained by Mark Casse and no protest was made.
"I said all week long that he was doing really well," a smiling Casse said of the 10-1 winner. "What can I say, it's just exciting."
He said second-favourite War of Will, ridden by Tyler Gaffalione, did not run his best race on Saturday.
"I could see War of Will was struggling," Casse said.
"He was maybe a little flat today and I saw jockey Joel (Rosario) cut the corner a little bit (on Sir Winston) and I could see where War of Will was getting a little weary."
The win was just the third in 10 starts for Sir Winston, who finished second in the Peter Pan Stakes at Belmont last month.
The race is the final leg of U.S. thoroughbred racing's Triple Crown, which was not up for grabs after Kentucky Derby winner Country House did not run in the Preakness due to illness. He did not compete at Belmont either.
The race caps a wild Triple Crown season that saw the first disqualification of a horse that crossed the line first at Churchill Downs and a rider thrown from his horse at the start of the Preakness.
The races were also contested amid growing controversy around the sport as 27 horses have died at Southern California's Santa Anita Park since the racing season began in late December.
The latest fatality came on Wednesday when two-year-old colt Derby River was euthanised after suffering a fractured shoulder, renewing calls for a suspension of racing at the venue.
(Reporting by Rory Carroll, editing by Ed Osmond/Greg Stutchbury)
