Even then, that might not be good enough if Korean K T Kim, Knox’s conqueror in testing conditions on the second day at Austin Country Club, makes it three wins out of three against Bill Haas in the other concluding match in the bracket.
In a clash between the two first-day victors, 17th seed Knox fell behind at the second to Kim, the last man into the 64-man field but who has chalked up 18 professional triumphs, and quickly found himself four down as his opponent reeled off three hole-winning birdies in a row from the sixth.
Scottish No 1 Knox, who had been pleased with his performance as he claimed a 3&2 success over Haas on Wednesday, rallied to win the ninth and 11th, where pars proved good enough on both occasions.
The Invernesian then lost the 14th to a par, when Kim rolled in an eight-foot putt, before being conceded the 16th but, with Knox unable to make a birdie from long range and his opponent safely on the green at the next, a handshake signalled a 3&1 defeat.
With only the top player progressing to the last 16, Kim is the favourite to go through and a half against Haas would be good enough for the 30-year-old. If both Haas and Knox come out on top, though, it would leave them on two points along with Kim and the winner of the group would then be determined by a play-off.
A fortnight before heading into The Masters as the defending champion, Willett crashed to a 6&5 defeat by Haas, having already suffered a 4&2 loss to Kim on the first day.
World No 2 and 2015 winner Rory McIlroy was handed an unexpected day off after his scheduled opponent, American Gary Woodland, withdrew due to a “personal family matter”. Woodland’s early exit came 24 hours after Jason Day, the defending champion, pulled out of the event to spend time with his mother as she undergoes treatment for lung cancer.
While McIlroy’s fate was still out of his hands – Dane Soren Kjeldsen, his first-day conqueror, needed only a half against Argentine Emiliano Grillo to advance to the last 16 – one player already through is Aberdeen Asset Management Scottish Open champion Alex Noren. The Swede made it two wins out of two with a 3&2 victory over Austrian Bernd Wiesberger before learning that his scheduled opponent in the final match, Italian Francesco Molinari, had joined the list of withdrawals due to a wrist injury. “I putted better than yesterday and that helps a lot,” said Noren, who won four times in 11 events in the second half of last season.
Others to chalk up second wins included world No 1 Dustin Johnson, 2013 Open champion Phil Mickelson and former Scottish Hydro Challenge winner Brooks Koepka, the latter having recorded a brace of 6&5 successes against Jason Dufner and Kevin Kisner.
Johnson, who is bidding to make it back-to-back WGC triumphs after winning the Mexico Championship earlier in the month, beat two-time major champion Martin Kaymer 3&2 in his second match. “I’m very happy to get two victories,” said the American. “I control my own destiny. If I win my own match (tomorrow), I win my bracket.”
Mickelson is also on course to progress after an impressive 5&4 victory over compatriot Daniel Berger, having already beaten Si Woo Kim 5&3.