At that stage, the US PGA champion from Zimbabwe led by two shots from Germany's Bernhard Langer with the next nearest challenger two strokes further away. Then Price took a six at the ninth, and nearly everyone else still on the Sawgrass course began to close in on him.
Payne Stewart, the former US Open and PGA champion, made one of the biggest moves, and his 66 was marred only by a bogey on the last hole to leave him with a 54-hole total of 206, 10 under par.
Stewart was delighted to be back in contention having not won a tournament since his US Open victory in 1991, and said: 'It was one of those days I've been waiting for, and for a long time, too.'
With only two holes remaining, Langer caught Price with a birdie two at the 17th, but he promptly gave the stroke back at the last when he missed the green to the right. Price then missed the final fairway, but salvaged his par to finish with a 71 for a total of 203 and a one-shot lead over Langer, Australia's Greg Norman and the American Mark O'Meara.
Another American, Paul Azinger, was a further shot behind on 11 under, just ahead of Stewart and fellow Americans Ken Green and Jim Gallagher Jnr.
Earlier, Britain's Ian Woosnam had come within a yard of ruining a fine round by losing his ball in the water on the 18th hole when the wind made him indecisive and he chose the wrong club.
But the former US Masters champion managed to save his par and complete a three under par 69 that left him on 210.
THE PLAYERS' CHAMPIONSHIP (Sawgrass, Ponte Vedre) Leading third-round scores: (US unless stated): 203 N Price (Zim) 64 68 71. 204 M O'Meara 67 71 66; G Norman (Aus) 66 70 68; B Langer (Ger) 65 69 70. 205 P Azinger 68 69 68. 206 P Stewart 70 70 66; J Gallagher Jr 69 69 68; K Green 70 67 69. 207 R Mediate 68 71 68; J Haas 69 70 68. 208 C Pavin 69 72 67; N Ozaki (Jap) 72 68 68; D Rummels 69 65 74. 210 I Woosnam (GB) 71 70 69; B Ogle (Aus) 70 72 68. 211 T Watson 70 72 69; T Johnstone (SA) 70 71 70; T Lehman 69 73 69; B Bryant 69 70 72.Reuse content