The 31-year-old American, who missed the cut in his three previous Opens, took advantage of a red-hot putter to make six birdies in a bogey-free round which equalled the Open two-round record aggregate of 130.
"I'm sure everybody in this room is in about as much of shock as I am right now," Snedeker told a packed news conference at Lytham.
"But I feel good. I played pretty well the first two days. No bogeys around here is getting some good breaks and playing some pretty good golf.
"My mantra all week has been to get the ball on the greens as fast as possible. Once I'm on there I have a pretty good handle on the speed of the greens. Just going to try and keep doing that over the weekend."
Snedeker sprung to prominence when he went into the final round of the 2008 U.S. Masters in second place but a closing 77 left him in a tie for third behind South African Trevor Immelman.
The winner of three U.S. Tour events was asked to describe himself.
"I'm a pretty happy‑go‑lucky guy," he said. "I'm very lucky to do what I do for a living. I've got a brother and family that keep me well in line, know where I am on the totem pole.
"I'm married with a 16‑month‑old little girl at home who pretty much dominates me and anything she wants to get she's going to get. That's the kind of guy I am. I'm very simple, not a frilly guy by any means."
Snedeker played a practice round at the 2008 Royal Birkdale Open with American Tom Watson, one of his boyhood heroes who won the world's oldest tournament five times.
"It helped a bunch playing with him," he said. "He told me the first time over here he wasn't a big fan of links golf. The second time he played he loved it.
"You've got to kind of embrace it, realise that you're going to get good bounces, bad bounces. Expect the worst and hope for the best."
Snedeker said in his first three Opens he was too used to playing American-style golf, attacking the pins and taking too many risks.
"This week I'm doing a much better job," he said. "I just want to make sure I don't put myself in a bad spot."
The tall, fair-haired resident of Nashville, Tennessee has so far avoided any of the 205 bunkers that protect the Lytham links.
"I came close a couple of times and got lucky," Snedeker said. "To hit it in no bunkers around here, you have to get lucky. I've gotten very fortunate when I was hitting bad shots and hadn't gotten in bunkers.
"I don't expect that stat to hold over the weekend. I'm fully prepared to hit it in a few bunkers."
Snedeker has been spotted in a local pub on a couple of evenings this week.
"I enjoy the local ales," he said. "The local beers are very good. I was not there late, you can attest to that. Might have been late there the first night but trying to get over the jet lag. I love being over here."