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.
After two early birdies and a bogey, Woods missed an eight-foot par putt at the par-5 eighth hole and seemed destined for an unspectacular round.
Scott, who has never led at Augusta despite winning the green jacket in 2013, was happy with his round.
"Three [majors] in a row, I've been right in the mix", Woods added, building on his second place at last year's PGA Championships.
McIlroy was also less than happy with his tee shot on the par-three fourth, but holed from 32 feet for an unlikely birdie, only to then drop shots on the sixth, seventh and ninth, where his approach plugged in the top of a greenside bunker.
"I feel like I played my own way back into the tournament", said Woods, who is seeking his first major victory since 2008.
With the crowd closing in on Woods after hitting his shot, the security guards rushed in to prevent the American from being crowded out.
"It was fun", Woods said after the round, before saying he was confident on how he was striking the ball ahead of the weekend. Had he made a couple of makable putts earlier in the round, including a four footer on 12 just after a brief weather delay, Woods could be tied for the lead. "Accidents happen, and we move on". After a flawless opening round, Koepka had two bogeys and a double in his first six holes on Friday but the twice U.S. Open champion was able to regain his composure, steadying himself with six straight pars from the ninth. "I'm in a good spot to kind of run with them". 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 risky par-3 12th.
It worked wonders as he appeared to be in considerably less pain while putting together a round that was almost flawless, although Day said his wife Ellie deserved just as much credit for his remarkable recovery.
Woods had three birdies on each nine, with a bogey 5 on the fifth his only blight.
USA left-hander Phil Mickelson, who at 48 would become the oldest major champion in golf history with a win, shot 73 in his 100th career Masters round to stand three off the lead.
Justin Hading, who surged to the top of the leaderboard for much of Round 1, was still in the hunt at six-under par.