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.
If that's not enough, Phil Mickelson and Justin Thomas were very much in the mix.
"This is really stacked," Scott said. "It's going to be an incredible weekend no matter what happens now."
Woods has gone 14 years since he last won the green jacket, 11 years since his last major and had five surgeries — four on his back, the other to rebuild his left knee. But he feels he's getting closer.
"The last three majors, I've been right there," Woods said.
He briefly held the lead Sunday in the British Open. He chased Koepka to the finish line in the PGA Championship. And now he goes into the weekend one shot behind, the closest he has been to a lead going into the weekend at a major since the 2013 British Open at Muirfield.
But that's not just anyone he's trailing. Molinari, the British Open champion who has shown he belongs among golf's elite, had a 67 and was the first to reach 7-under 137. Day was right behind, coping with nagging soreness in his lower back with a 67 to match the Italian.
Koepka, the US Open and PGA champion, began with a birdie to quickly take the lead, only to hit out of the pine straw, off a tree and into the creek to make double bogey on the par-5 second hole. He made two more bogeys before reaching the seventh hole, and then pulled himself together to salvage a 71.
"You are going to be tested in a major championship one way or another," Koepka said. "I hit a bad shot; just got to suck it up and just keep going on. You've got a lot of holes left and you can make up some ground. Thankfully, it wasn't on the 18th hole where you need a par to win or something. Just got to keep battling and see where I leave myself [today]."
Scott was the only player to reach 8 under with a 2-iron into 5 feet for eagle on the 15th, only to miss a 3-foot par putt on the 16th. It added up to a 68 for the Australian who won the Masters six years ago, and has gone three years since his last victory.
He had a chance to win the PGA Championship in his last major until Koepka pulled away and Scott made a careless bogey at the end to finish third. He has shown flashes this year on the West Coast, at Torrey Pines and Riviera, but has geared his game towards this week.
Here he is, with a lot of company.
"Look, [today] is a very important day because there's no doubt someone in the top 15, or a few of them, are going to play very well," Scott said. "This is the best players in the world on the biggest stage that we all want to be in so badly."
The only scare for Woods came on the 14th hole, when his drive went well left into the trees. The shot was pure, hooking around the pines to the green.
On his quick walk to the fairway to see where the shot finished, a Georgia Bureau of Investigation agent rushing over to control the spectators behind Woods slipped on the rain-slickened grass and slid into Woods' right leg.
Woods hopped out of the way, winced and repeatedly flexed his ankle, and then poured in another putt.
He did not show any trouble the rest of the way, and didn't find much interest in talking about it after his round except to say "accidents happen" and "it's all good". He was particularly happy to finish, especially after storms moved into the area and stopped play right after his tee shot into 5 feet on the dangerous par-3 12th.
The delay lasted only 29 minutes. Woods returned to miss the putt, and then took three shots from 35 feet behind the par-5 13th green to lose another prime birdie opportunity. But he made up for them with a couple of long birdie putts, and he had no complaints with his position.
"I feel like I played my own way back into the tournament," Woods said. "I was just very patient [yesterday], felt very good to be out there doing what I was doing. This is now three straight majors I've been in the mix and so it's good stuff."
Mickelson stumbled to a 73 but still was only three shots behind. Bryson DeChambeau, who shared the 18-hole lead with Koepka, went bogey-double bogey around the turn and shot 75. He still was within four shots, along with Justin Thomas, who had a 68.
As for Rory McIlroy, the career Grand Slam might need to wait another year. McIlroy played the par 5s in even — two bogeys, one par and an eagle on No 8 that got him under par, but only briefly. He was only seven shots behind but had 35 players in front of him.
Masters at a glance
• Leading: Francesco Molinari, Jason Day, Brooks Koepka, Adam Scott and Louis Oosthuizen at 7-under 137.
• Just behind: Dustin Johnson, Justin Harding, Xander Schauffele and Tiger Woods were a shot back.
• And Phil? Phil Mickelson headlined a group of four players at 140.
• Long leg of the law: Tiger Woods was nearly slide-tackled shortly after playing a shot well off the 14th fairway by a law enforcement officer who fell and slid while rushing to his side to hold off a surge by fans.
• Notable: Four amateurs made the cut, including Vikor Hovland of Norway, who leads the quartet at 1-under 143.
• Lost my homework: Bryson DeChambeau — "the Mad Scientist" — fell out of a tie for the lead after the first round with a 75.
• Quotable: "Unfortunately, there's a leaderboard on almost every hole, so you can always know where you're standing among the leaders." — Schauffele on his round.
- AP
