Woods, champion here four times in his last seven starts, struck the clubhouse roof with his approach to the par-four ninth and was fortunate to get a free drop before completing a six-under-par 64.
That left him at nine-under 131, one stroke clear of fellow American Davis Love III (65) and ideally positioned to win his fourth consecutive PGA Tour title.
Woods swept past overnight leader Adam Scott with four birdies in his first four holes and picked up three more shots after the turn before dropping his only shot of the round at Firestone Country Club.
Australian Scott, two ahead at the start of the day, produced an erratic display before bogeying two of the last three holes for a 71 and a tie for third at six under with American Jim Furyk (65).
Rules officials deliberated for more than half an hour before learning that a youngster had pocketed Woods's ball after finding it in the service area behind the clubhouse.
With the clubhouse not deemed out-of-bounds and the grandstands in front a temporary immovable obstruction, Woods was able to take a free drop 84 yards from the hole, close to the first tee.
South African Ernie Els shot a 67 to share fifth place at five-under 135 with Americans Lucas Glover (69) and Kevin Stadler (67).
Of the other big names, Jose Maria Olazabal carded a 70 to lie joint 11th at two under, four strokes better than fellow Spaniard Sergio Garcia, who fell back with a 73.
Masters champion Phil Mickelson bogeyed his first four holes on the way to a second successive 74 and 68th place at eight over.
Seventy-eight players, including 47 of the world's top 50, are playing in the limited-field event.
Leading second round scores:
131 – Tiger Woods (US) 67, 64.
132 – Davis Love III (US) 67, 65.
134 – Adam Scott (Australia) 63, 71; Jim Furyk (US) 69, 65.
135 – Kevin Stadler (US) 68, 67; Lucas Glover (US) 66, 69; Ernie Els (South Africa) 68, 67.
136 – Luke Donald (Britain) 67, 69.
137 – Stewart Cink (US) 70, 67; Robert Gamez (US) 70, 67.
138 – Vaughn Taylor (US) 71, 67; Jose Maria Olazabal (Spain) 68, 70; Brad Faxon (US) 69, 69; Angel Cabrera (Argentina) 70, 68; Michael Campbell (New Zealand) 67, 71; J.J. Henry (US) 70, 68; Paul Casey (Britain) 69, 69.
139 – Thomas Bjorn (Denmark) 72, 67; Stephen Ames (Canada) 69, 70; Trevor Immelman (South Africa) 69, 70; Zach Johnson (US) 71, 68; Justin Leonard (US) 70, 69.
140 – Chris DiMarco (US) 68, 72; Mike Weir (Canada) 69, 71; Ben Crane (US) 73, 67.—Reuters