Knox, who had opened with a two-under-par 70 to start the day alongside Woods, covered the front nine in 32 and also birdied the 10th and 16th but three-putted the 17th and also bogeyed the last after a wayward drive.
That left the Invernesian having to settle for a 68 and a six-under-par total, leaving him three shots off the clubhouse lead, held by Jim Furyk after the 2018 US Ryder Cup captain rolled back the years with a stunning 64.
Woods began the second round five shots off the lead but had moved ominously up the leaderboard with birdies on the 12th, 13th and 16th, having started from the 10th tee.
However, the former world No 1 one then dumped two balls into the water on the par-three 17th on his way to a damaging quadruple-bogey seven.
Woods had narrowly avoided the water on the 13th and 16th and made birdie on both occasions, but his luck ran out on the 17th when his tee shot pitched on the green but just trickled off the back edge.
The 43-year-old opted to play his next shot from the drop zone but a pulled approach took one bounce before plunging into the water and, after finally finding the green, Woods two-putted from 20 feet.
“The second wedge didn’t really surprise me, it was too flat. The first one I hit surprised me,” Woods told reporters. “I was pretty ticked. I was determined to get it all back.
“Other than 17 I really haven’t done a whole lot wrong. Anyone who makes the cut has a chance.”
Woods regrouped to play his remaining 10 holes in two under par and return a 71, but on three under par, he was six shots behind surprise clubhouse leader Furyk, who carded eight birdies in his bogey-free effort. “I’ve had some good weeks here, almost won five years ago, and I’ve also had some rough weeks here and that’s the nature of this golf course,” the 48-year-old Furyk told Sky Sports.