Despite missing two birdie chances inside 8 feet on the back nine, he holed consecutive 30-foot birdie putts for a 4-under 68. "I know I can play this golf course, just this week I have not played it well enough".
Woods was tied with Dustin Johnson, another major champion and world No. 1, along with Xander Schauffele and Masters newcomer Justin Harding of South Africa.
Dustin Johnson (70) and Justin Harding (69) were a shot behind at 6-under, alongside four-time Masters victor Woods, who is sitting ominously just behind the leaders as he hunts a first major since the 2008 US Open.
Pre-tournament favourite Rory McIlroy has plenty of work to do after he shot 71 to sit seven off the pace at even par, while world number one Justin Rose and the respective Masters champions of 2016 and 2017, Danny Willett and Sergio Garcia, all missed the cut at four over.
Seventh-ranked Molinari fired a bogey-free 67, the lowest score of his 26 career rounds at Augusta National, where his best finish was a share of 19th in 2012.
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McIlroy needs a victory at Augusta National to join Gene Sarazen, Ben Hogan, Gary Player, Jack Nicklaus and Tiger Woods in having won all four major championships. The shot was pure, hooking around the pines to the green.
Woods would go on to birdie the hole, so the effect of the slide wasn't immediate.
He managed to keep his balance, winced, hobbled and flexed his ankle repeatedly when he made it to the fairway.
"Accidents happen, we move on", Woods said of the incident, confirming he suffered no major damage from the guard's boot.
The delay lasted only 29 minutes.
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A stunning eagle launched Australian Adam Scott past countryman Jason Day into the outright lead at the Masters, before a three-putt on the next hole brought him back as rain lashed a weather-interrupted second round.
"I feel like I played my own way back into the tournament", Woods said.
"I put myself in a good place for the weekend", Scott said.
Poulter enjoyed a massive slice of luck when his approach to the 13th stuck in the bank of Rae's Creek and allowed him to chip and putt for an unlikely birdie, but added: "I'm a little frustrated with a couple of missed opportunities towards the end there. This is now three straight majors that I've been in the mix and so it's good stuff". Bryson DeChambeau, who shared the 18-hole lead with Koepka, went bogey-double bogey around the turn and shot 75.
But since then he has shown more than a glimmer of his once-spellbinding form, and has placed himself firmly in contention with a commanding 68 in his second round to remain a shot behind the leaders at 6-under par.
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The Lakers, who have been playing without James in the lineup for weeks, lost 104-101 to Portland following Johnson' announcement. Los Angeles has now missed the playoffs for six straight seasons. "We know that because it's Los Angeles".
The Queenslander, who received medical treatment on course beside the second hole on Thursday, came out firing on Friday with a round of 5-under par, rocketing him to seven under.