(CNN) -- Troubled golfer Tiger Woods has given Phil Mickelson every chance to claim his No. 1 ranking after failing to bounce back from his poor start to the WGC-Bridgestone Invitational on Friday.
Defending champion Woods will lose his position as the world's top player if Mickelson finishes fourth on Sunday, as he is currently outside the top-37 following his second round of two-over-par 72 in Akron, Ohio.
Mickelson kept his cool to shoot 68 and tie for second, joining veteran fellow American Justin Leonard on six-under 134 -- one shot behind South Africa's Retief Goosen, who also fired a 66 to set the early second-round pace.
Woods shot 74 on Thursday, his worst score on the Firestone course where he has won a record seven times before, and then fell apart after a solid start on Friday.
Starting on the back nine, the 34-year-old picked up a birdie at the par-three 15th but then dropped three shots in four holes from 18 and finished birdie-bogey-birdie-bogey.
That left him right at the back of the 81-player field, tied for 72nd after 36 holes.
Woods, who has been at the summit for 270 consecutive weeks and 612 in total, was 13 shots adrift of Goosen.
In some consolation, world No. 3 Lee Westwood -- who also had a chance of taking the No. 1 spot this week -- had an even worse day as his 76 left him one shot behind playing partner Woods on 147 overall.
The Englishman subsequently withdrew from the tournament, citing his ongoing calf injury problems, and is now expected to miss next week's PGA Championship at Whistling Straits in Wisconsin.
"I will be out for as long as it takes to get right. Hopefully it will be in time for the Ryder Cup [in October,]" the 37-year-old told the PGA Tour website.
And as there is no halfway cut in the World Golf Championship events, Woods can still climb up the leaderboard and make life difficult for Mickelson.
Masters champion Mickelson birdied three of his first six holes and then bounced back from a double-bogey at 14 with two more at 15 and 16 before a stunning bunker shot at the last to save par.
He and 1997 British Open champion Leonard were one shot ahead of Sweden's Peter Hanson (66), fellow American Bo Van Pelt (68) and first-round leader Bubba Watson.
Watson paid for his risky tactics as he offset three birdies with two bogeys and a double.
American Ryder Cup hopeful Anthony Kim was way back in 79th on his return after thumb surgery three months ago, adding 76 to his first-round 75.
Since finishing in a tie for fourth in his comeback at the Masters following revelations about his extra-marital affairs, Woods has struggled to regain the form that has seen him dominate golf for the past decade.
The richest sportsman in the world according to Forbes and Sports Illustrated, he missed the cut for just the sixth time in his career at the Quail Hollow Championship in late April.
After a break to recover from a neck injury, he then tied for 48th at the British Open on the St. Andrews course where he had twice before won the prestigious major event.