In contrast to last year's event when they were disqualified - Faldo for signing for an incorrect score and Price for moving an advertising hoarding - they shot 67s, five under par, to open up a four-shot lead in the challenge to win golf's biggest winner's cheque.
Faldo and Price thought they had ended the day only two ahead, but the defending champion, David Frost, was penalised two strokes following an incident on the 10th green.
Frost stood over an eight-inch putt for his par five, but as he addressed the ball it moved. That was a one-shot penalty, but by not putting it back in its original position, he incurred another.
Faldo, who shot 75 in the eve-of-tournament pro-am, said: 'It's nice to be up there. The heat was pretty stinking and I was drinking at least one bottle of water every hole.'
Ian Woosnam's chances of landing the million-dollar jackpot look slim. The Welshman managed only a four-over-par 76 and is joint last of the 12 competitors in the event, nine strokes adrift.
MILLION DOLLAR CHALLENGE (Sun City, Bophuthatswana): Leading first-round scores: 67 N Price (Zim), N Faldo (GB). 71 M McNulty (Zim), C Pavin (US), D Frost (SA). 72 F Allem (SA), B Langer (Ger). 74 M O'Meara (US). 75 P Stewart (US). 76 L Janzen (US), I Woosnam (GB), E Els (SA).