On an overcast morning at Augusta National, four-times champion Palmer, three-times winner Player and Nicklaus, who won a record six green jackets, hit the ceremonial first shots at the par-four opening hole.
Palmer struck a solid blow up the middle before fellow golfing great Player out-drove him by around 50 yards, his ball ending up above the crest of the hill on the right side of the fairway, some 250 yards from the tee.
Nicklaus hit the longest drive of the three, his ball rolling into the first cut of rough on the left before settling several yards ahead of Player.
"The only nerves you have are to make solid contact," a smiling Nicklaus, 73, said afterwards. "It doesn't matter diddly-darn where it goes."
Palmer, however, was delighted with his effort.
"It was my best drive of the year," the 83-year-old quipped.
Ten minutes later, 1988 Masters champion Sandy Lyle of Britain struck the tournament's first competitive shot by teeing off at the opening hole. Lyle was then followed by Americans John Peterson and amateur Nathan Smith.
American left-hander Watson, who won last year's title in a thrilling play-off with South African Louis Oosthuizen, was scheduled to tee off with Britain's Ian Poulter and US amateur champion Steven Fox at 10:34 local (15:34 UK time).
Four-times champion Tiger Woods, who has won three tournaments in just five starts on the 2013 US PGA Tour, has been grouped with Englishman Luke Donald and American Scott Piercy.
Though world number one Woods has not triumphed at the Masters since 2005 and is hunting his first Major crown in five years, he has been installed as a 4-1 favourite by Ladbrokes for the season's opening Major.
Woods and his playing partners start at 10:45 (15:45), one group after Watson and company.
In other groupings, three-times champion Phil Mickelson sets off with Oosthuizen and Germany's former world number one Martin Kaymer while 2011 winner Charl Schwartzel of South Africa has been paired with US Open champion Webb Simpson and Swede Peter Hanson.
Northern Irish world number two Rory McIlroy, American Keegan Bradley and Swede Fredrik Jacobson will tee off in the penultimate group of the day, behind Mickelson, Oosthuizen and Kaymer.