Woods' second birdie of the day was a quick turnaround from the previous two holes, where a bogey on each saw Woods fall three shots behind reigning British Open champion Molinari.
Immelman shot a par round 72 to make the cut for the first time since 2013 on two-over, while Grace is a shot behind.
At that point, he was three clear, but Molinari finally faltered on the seventh - dropping his first shot in 50 holes to fall one short of Stuart Appleby's record for the longest bogey-free streak at the Masters.
Woods was impressive during a 67 that left him tied second at 11 under alongside American Tony Finau, who carded an equal day's best 64, while three-time major victor Brooks Koepka (69) is fourth at 10 under.
Adam Scott admits he'll need an historic final round to win a second Masters title after he and countryman Jason Day blew golden chances to start the final day in serious contention. Former UCLA star Patrick Cantlay also shot 64 and was tied for 14th.
A severe weather forecast for Sunday afternoon has prompted Masters officials to move up the tee times for the final round at Augusta National.
Play will begin at 9:30pm (AEST) with the leaders to tee off at 11:20pm (AEST).
Solskjaer confident Phelan will remain alongside him at United as No 2
We are Manchester United , even if they are Barcelona - we are Manchester United , and we play in the Champions League just like they do.
But standing in his way is an inspired Open champion in the shape of Francesco Molinari, who played with Woods in the final round at Carnoustie a year ago on his way to lifting the Claret Jug.
"As a kid I always wanted to compete against him", said 29-year-old Finau of Woods.
Woods noted that three of his four Masters victories - in 1997, 2001 and 2002 opened with rounds of 70.
Even United States President Donald Trump, who has golfed with Woods at his Mar-a-Lago resort, said on Twitter he was looking forward to Sunday's final round. "That's where my advantage is, anyway, but in emphasis here at Augusta National".
He methodically rolled in putts of six, eight and nine feet to birdie the next three - and maintained his two-shot edge by getting up and down for par from a bunker at 18. "I've historically played the front nine really well and that sets up an easier time on the back nine. I could shoot 61, especially with the pins tomorrow", Scott said.
"I putted well today", Woods said.
They first met, he recounted, at Woods' restaurant in Jupiter, Fla., in 2015, when Finau was a PGA Tour rookie and Woods hosted a dinner for all of the Nike staff players.
"When I was on the Ryder Cup team and I surrounded myself with the other 11 guys and our captains, being in that locker room, it gave me an extra sense of confidence".