Fred Couples, the winner that year, was the early leader before Glen Day, a former regular visitor to the European Tour, eagled the last to lead by one with a six-under 66. Day, from Little Rock, Arkansas, finished two, two.
He birdied the 17th, with its famous island green, and then holed his second shot, from 180 yards with a seven-iron, for the first eagle at the 18th in the 16 years the tournament has been played on the Stadium Course.
Day's feat only compounded a largely bad day for the Europeans. Ian Woosnam had to retire after 12 holes, when he was five over, with a lower back injury, while Bernhard Langer, who, like Monty, has a fine record here, never recovered from taking a triple-bogey and a double in his first four holes.
Woosnam may now rest rather than go to New Orleans next week in order to be fit for the US Masters in two weeks' time. The three-times Augusta champion, Nick Faldo, who missed the cut last week, faces the possibility of doing so again after an opening 75, while Lee Westwood and Darren Clarke, both playing here for the first time, had 74s.
They were not the only ones to struggle on a difficult day for scoring. Tiger Woods had a level-par 72, while Ernie Els, despite getting to four under with six to play, had a 71.
Montgomerie, who teed off at the 10th late in the afternoon, started well enough with birdies at the 11th and 12th. But with a wedge in his hands at the 15th, the Scot left his approach 20 feet away and took three putts.
At the next, a par-five, he took four to get down from 100 yards for a six and then he bounced off the green into the water at the 17th to take a double-bogey five. Montgomerie halted the run with a 20-foot par putt at the 18th, but then promptly bogeyed the first before responding by birdieing the next two.
Couples does not appear on many leaderboards these days, which may be because he does not play that often. Couples either blows hot or cold, nothing in between, but when he is on, watch out. This might be only the American's sixth appearance of the season, but he has already once - at the Bob Hope Classic. That was his first win since his second win here in 1996.
Problems in his personal life, including the death of his father, plus continuing back trouble left Couples winless last year, but the old instincts are still there.
While the defending champion, Steve Elkington, was forced to withdraw on Tuesday after not recovering from sinus surgery in time, his countryman Greg Norman did not make it to the first tee either. Norman, the Sawgrass tournament record holder at 24 under par, aggravated an old injury in his left shoulder and was advised to rest.
PLAYERS' CHAMPIONSHIP (Sawgrass, Ponte Vedra, Florida) Early leading first round scores (US unless stated): 66 G Day. 67 F Couples. 68 J Kelly. 69 N Ozaki (Japan), B Mayfair, B Crenshaw, B Lietzke, P Mickelson, M Calcavecchia, D Duval, D Frost (SA), J Maggert. 70 T Tryba, J Furyk, B Andrade, M O'Meara, L Jansen, R Black. 71 S Jones, T Watson, J Cook, J Daly, D Toms, N Price (Zim), C Stadler, T Armour, E Els (SA), S Cink, R Goosen (SA), R Damron, S Ames (Trin), S Pate, B Faxon, D Barron. 72 J Parnevik (Swe), J M Olazabal, D Sutherland, J Huston, F Nobilo (NZ), T Woods, P Blackmar, R Cochran, B Estes, J M Olazabal (Sp), S Gump, B Chamblee, Lee Rinker, O Uresti, J Parnevik (Swe), B Tway, S McCarron. 73 F Funk, M Brooks, M Hulbert, C Parry (Aus), M Standly, D Edwards, B Henninger, S Hoch, W Wood. Selected: 74 L Westwood (GB), D Clarke (GB). 75 N Faldo (GB). 76 C Rocca. Withdrew: G Norman (Aus), I Woosnam (GB).Reuse content