Woods produced a 36-hole total of 13-under 127, giving him a massive seven-shot lead over Keegan Bradley and Chris Wood.
After seeing his tee shot at the par-4 13th hit a tree and bounce back in the fairway, Woods found the green from 218 yards away and then holed a 14-foot putt for birdie that left him at 9-under for the round.
Two birdies over the final five holes would have given him the sixth 59 in the history of the tour and three birdies would have produced the circuit's lowest 18-hole score ever.
Instead, he had to scramble for par at the 14th, missed a 10-foot birdie effort at the 15th and had to settle for pars at the next two holes. It took a 25-foot par putt from the fringe at the final hole for Woods to shoot a 61, which he had done on three previous occasions.
"I had it going today," Woods said. "It was a nice start and I just let the round build from there."
Phil Mickelson, fresh off his wins at the Scottish Open and British Open, shot a 71 for a two-day total of 143. Brand Snedeker, a winner last week at the Canadian Open, was at 140 following a 70.
Although Woods has not won a major title in five years and still is four shy of the all-time record in that department held by Jack Nicklaus, he is nearing another of the sport's major marks.
A win this week would give Woods his fifth tournament crown of the year and 79 on the PGA Tour. He would need three more wins to equal the career record held by Sam Snead.
Woods currently shares another record with Snead, having won the Arnold Palmer Invitational eight times. Snead also had eight victories at the Greater Greensboro Open.
If Woods captures this week's title, it will be the eighth time he has won this tournament. That would make him first player in tour history with eight wins at two different events.