First round leader Watson birdied his first two holes of the day to move to seven under, but there was no such joy for Goosen who needed seven shots on the par four first.
That sent him back to four under for the week, with Justin Leonard and Phil Mickelson remaining second on six under in Akron, Ohio.
Mickelson, who will almost certainly become World Number One with a top four finish on Sunday after Lee Westwood's withdrawal and Tiger Woods shooting a third round 75, opened with a bogey but holed from six feet at the third to get the shot back.
Leonard and Mickelson were joined on six under by England's Oliver Wilson when The Ryder Cup player birdied the ninth for an outward 31.
Wilson is yet to win a European Tour event but by opening with a hattrick of birdies he gave himself every chance of lifting the trophy at Firestone.
Katsumasa Miyamoto earlier completed a best of the week 62 to set the clubhouse benchmark at five under, while out on the course South Africa's Ernie Els and Swede Peter Hanson were amongst those on the same score.