Defending champion Tiger Woods fired a stunning seven-under-par 65 to equal Hoylake's course record and secure a one-shot lead at the 135th Open.
Woods is bidding to lift his third Claret Jug on Sunday
The world number one, who resumed on five under, made his move with an eagle and six birdies to reach 12 under.
He leads by one from Ernie Els and three from Chris DiMarco, both of whom matched Woods's mark of 65.
World number two Phil Mickelson could only muster a 71 and is eight shots behind Woods going into the weekend.
Former Open champions John Daly and Ben Curtis both missed the cut, as did former Masters champion Fred Couples.
Daly, who won at St Andrews in 1995, was cruising going into the 18th but is heading home after a triple-bogey left him one over.
Curtis, the 2003 champion, carded a 73 to finish on two over alongside Couples, who made seven bogeys in his 76.
However, America is well represented at the top of the leaderboard, with Jim Furyk (71), Ben Crane (71), Jerry Kelly (67) and Mark Calcavecchia (68) all at five under.
Woods plays with the 'Tiger Show' for 72 holes. Whoever plays with him now will have to cope with that
Woods, who ended his first round with an eagle, was leading by three before Ernie Els matched his 65 in the afternoon to close to within one shot.
The 10-time major winner was delighted with the way he played, especially his eagle at the 14th when his four-iron approach pitched in line and bounced into the hole.
"I made a few bombs and obviously 14 helped a lot," Woods told BBC Sport.
"I could not see the flag from where I was and I was just trying to hold it straight against the wind.
"Trust me I was just trying to get the ball on the green and take my four so to make two was a bonus."
The world number one, playing only his third tournament since the death of his father Earl, missed just one fairway during his round and was in magnificent form with the putter.
The 30-year-old's form made some pundits write off the rest of the field but Woods said it was far too early to claim victory.
"I'm not here with the jug," he said. "We've got 36 more holes to go. Unless there's some kind of rainstorm coming and it's cancelled after two days, we have a long way to go."
Woods' playing partner Nick Faldo believes the American is on course to break the record 19-under score he set at the Open in 2000.
Tom Watson's 70 means he is still around at the weekend
Faldo, who crashed out on four over, also said Woods could become the first player to retain the Claret Jug since Tom Watson in 1983.
"If he keeps cruising I predict he gets to 20 under," said Faldo. "He is the best competitor, mentally the toughest and the most trained for what he has to put up with.
"He plays with the 'Tiger Show' for 72 holes. Whoever plays with him now will have to cope with that."
The 37-year-old DiMarco, two under overnight, got off to the perfect start with birdies at the first two holes.
He strengthened his position with four consecutive birdies around the turn and then traded shots on the 15th and 17th before finishing with a birdie at 18.
DiMarco insisted there was never a chance of him missing the Open, despite the recent death of his mother.
"I don't think it was ever an option not to come, my mother would not want that. If I missed it because of grieving she would have been very upset," he said.
"She was a very special lady and I'm going to miss her a lot but it's very therapeutic for my father to be here with me."
Masters champion Mickelson endured a frustrating day and will have his work cut out on Saturday to get back in touch with Woods and Els.
"I'm obviously not excited about being eight shots back," Mickelson said.
"But I still feel that a good round tomorrow will give me a chance on Sunday, and that's the goal."
Mark O'Meara, Open champion in 1998, is three under after a second-round 70.
David Duval, Open champion in 2001, carded a second successive 70 and is four under going into the weekend while 2004 winner Todd Hamilton (71) is one under.
Five-time winner Watson, 56, booked his place for the weekend after a second-round 70 left him on two under overall.