With one hole of his third round remaining, the 30-year-old is a shot behind leader Kevin Kisner, as are Dustin Johnson and China's Haotong Li.
Kisner leads on 16 under after shooting a two-under-par 70 on Saturday.
Jordan Spieth, who is hoping to return to world number one, had a nine-under 63 to move to 13 under overall.
Spieth began the day 10 shots behind Kisner, but carded nine birdies to move three adrift of his fellow American, who had his first bogeys of the week.
On a day when play was delayed because of the weather, the final group of Knox, Kisner and Branden Grace were asked on the 18th tee if they wanted to play the hole.
Knox opted not to, while Grace carded a birdie to finish on 12 under and Kisner had a par.
Northern Ireland's Rory McIlroy is eight under after a four-under 68.
With Knox choosing not to finish in the dark, he will have to return on Sunday to play the par-five 18th.
"I played beautifully the first 12 or 13 holes and then I started to limp in a little bit so I decided not to play the last hole because it was awfully dark," said Knox, from Inverness.
"Branden and Kevin wanted to get done. It was into the wind and I was like, maybe I'll just wait until the morning and see if I can catch it downwind or no wind.
"I was happy with my decision. My caddie didn't want me to play the last.
"I'm going to have to wake up a lot earlier, starting at 7.45 and I won't tee off again until probably 10.45. It's going to take the best round of my life, so I'm going to have to go for it."
Spieth, playing in his first tournament for two weeks, showed signs of rustiness as he shot 68 and 72 in his first two rounds but was close to his best in his third.
"This will be the first and only time I would say this, but I was not expecting to be in this position come Sunday when the week started," said the American, who needs to finish in the top 13 to reclaim the world number one ranking from Jason Day, who is absent as his wife is due to give birth to their second child.
"I've struggled to shoot lower than two or three under on this golf course in the past couple years, but Saturday was the day to do it with ball in hand, very little wind and some gettable pins.
"I missed four putts inside eight feet - I'm not going to complain about the round but I felt like the way I played could have been 10 or 11 under, for sure."

The National Statistics Institute said the number of unemployed Spaniards fell by 12.4% to 4.78 million last year, thanks to a strengthening economy.
In the fourth quarter the rate dropped to 20.9% of the workforce, compared with 21.2% three months earlier.
The figures, which are better than predicted, are at their lowest level since mid-2011.
The economic recovery pushed the number of unemployed people down by 678,200 for the whole year.
But there is concern that much of the growth depends on short-term jobs
The data showed almost twice as many temporary posts were created in 2015 than permanent ones.
Vincenzo Scarpetta, a  political analyst at Open Europe in London, said: "If the economic cycle starts going less well, those jobs could start to evaporate."
Economists fear that the inconclusive election, which has yet to result in a government, could delay much needed reform of the labour market.
Spain has suffered a double-dip recession that pushed unemployment to just under 27% at the end of 2013.
Retail sales grew 3.6% in 2015 as a whole, which is the biggest rise in 15 years.
A fall in the active workforce also helped the drop in the unemployment rate in the fourth quarter, reflecting the flow of workers going abroad and inactivity among the long-term unemployed.
Scot Russell Knox was one shot off the lead when the third round of the WGC-HSBC Champions event in Shanghai was suspended because of darkness.
[NEXT_CONCEPT]
Spanish unemployment figures have experienced their biggest annual fall but unemployment remains at over 20%.