After rounds of 66 and 67, Davis had a 69 to sit at eight under and tied for 12th at the St. Jude Championship in Memphis, six shots behind leader Lucas Glover.
The American's four-under 66 gave him a one-shot lead going into the final round at TPC Southwind and a chance to lock up his spot in the Tour Championship.
"I'm in a good spot. Just iron a few things out and wake up tomorrow a little more confident than I am right now and see where we are," Glover said.Â
Davis' mixed round included four bogies, three birdies and an eagle on the par-5 16th to keep him on track to taking part in Chicago, Illinois.
The top 70 players from the season-long FedExCup points race are competing in the $US75 million ($A115 million) playoffs, and only the top 50 in the standings after this tournament will advance to next week's field.
"It was a bit of a grind today, Davis said.
"I didn't quite have my stuff off the tee, which made it a lot more difficult trying to get the ball on the green in regulation. Hung in there well, had a little stretch on the back nine to get myself back sort of in it, and yeah, still a chance to get to next week with a good round tomorrow.
"I don't really want to look at that (next week) until after the round tomorrow. I'll put my head down, try to make as many birdies as I can and see what happens at the end of that."
Fellow Australian Jason Day (72) is two over and out of the reckoning, while 43-year-old former US Open champion Glover has now shot in the 60s in 20 of his last 21 rounds. Three of those came last week when he won the Wyndham Championship to go from No.112 in the FedEx Cup and well into the top 70 who reach the PGA Tour's post-season.
Fellow American Taylor Moore (65), who won his first PGA Tour title earlier this year at the Valspar Championship, bogeyed his last hole to trail by one.
He birdied three of the par 3s and was tied for the lead on two occasions on the back nine until poor drives led to bogeys.
England's Tommy Fleetwood (66) had three birdies over his last five holes to be two off the pace as he goes after his first win on American soil.
Max Homa ran off three straight birdies on the back nine for a 65, while Jordan Spieth had to settle for a 68. They were both three back at 11 under.
Spieth began the post-season at No.31 and has plenty at stake on Sunday, for the FedEx Cup and possibly securing one of the six automatic spots for the Ryder Cup.
Rory McIlroy (68) and Patrick Cantlay (66) were among those five shots behind.
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