Olesen followed an opening nine-under 62 on Thursday with a 66, hitting out of the rough to set up a five-foot birdie putt on his final hole - the par-4 ninth.
The 35-year-old Danish player also recovered from a double bogey on the par-4 15th with consecutive birdies as he searches for his first PGA Tour victory.
"I think both days, my iron play has been really, really good," Olesen said. "I hit a lot of shots really close to the pin and gave myself a lot of good chances.
"Today, there was like two or three bad drives that cost me, but I still felt pretty good over the ball."
He had a 14-under 128 total.
Knapp shot 65. Pierceson Coody (65) was another stroke back with Sam Stevens (68). Stevens closed with a bogey on No.9. Takumi Kanaya (64), Chris Kirk (67) and Matti Schmid (68) were 11 under.
With two weeks left in the regular season, Knapp (55th in the FedEx Cup standings), Schmid (68th) and Kirk (77th) remained in contention for the FedEx Cup Playoffs. The top 70 advance to the first playoff event.
Australia's Adam Scott fired a four-under 67 to move to six under and 33 places up the field.
The ultra-consistent Scott has made the playoffs in 17 out of 18 seasons, but is currently 85th in the standings.
The former world No.1 and 2013 Masters winner is the only Australian left in the field, the rest failing to make the five-under cut.
Cam Davis shot a 71 for a one-over total with the result dropping the Sydneysider four positions in the standings to 69.
Karl Vilips also had a 71 for his one-under total. The West Australian also lost ground in the standings, declining two spots to 83.
Olesen is a European tour regular with nine international victories. He missed the cut last week in the British Open in Northern Ireland.
"I take every week as it comes," Olesen said. "Every week is an opportunity to try and bounce back and do something special."
Knapp remained bogey-free through 36 holes for the first time in his career, starting out with birdies on Nos.10-12. He seeks his first PGA Tour win of the season after earning the first of his career in the 2024 Mexico Open.
"I feel like it's been ... kind of mistake-free for the most part," Knapp said. "I haven't really had to scramble too much."
Knapp had the lowest score on the PGA Tour this year, a 59 at the Cognizant Classic in February.
Adam Svensson nearly matched Knapp with a course-record 11-under 60 on Thursday, but dropped 29 spots Friday with a 75.
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