Lee, the former world No 1 amateur began his round on the 10th and made eagle on 11 before back-to-back birdies on 16 and 17 to make the turn in four-under 32.
He kept up his momentum through the turn as he made a birdie at one, an eagle at two and then added birdies on five and seven, one of the signature holes at Pebble Beach, to come home in 31 and post a 63.
It could have been even better as the former US Amateur champion lipped out for birdie on the eighth, his penultimate hole, and left his birdie shot short on his last to finish at nine under.
It is a standout highlight on the PGA Tour for the 21-year-old who made his name by making a hole in one in his second event at the Humana Challenge in California two weeks ago.
Lee, who is the first New Zealand golfer to play on the PGA Tour since Tim Wilkinson in 2009, feels like he has a big year ahead after an up-and-down start to 2012.
"The year is only just starting. It is only February right now. I guess I was too nervous and not focusing on my own game so I just learned a way to play a little bit better than what I was used to over the last four weeks.
"I was playing good the last four weeks, it just didn't really happen for me. I'm starting to play really good."
He believes the very competitive nature of the Nationwide Tour, where golfers have to card low scores just to make the cut, helped shape his round at Pebble Beach.
"I was actually struggling for a couple of years and [the Nationwide Tour] taught me how to make low scores, especially out here. You've got to make them."
It wasn't as rosy, however, for fellow Kiwi Michael Campbell, who continues to struggle in 2012. He fired an eight-over par 81 at the Dubai Desert Classic.
The 2005 US Open champion, who has missed his first two cuts of the year in the United Arab Emirates, began well with a birdie at the second but fell apart with five bogeys and two double bogeys to be 18 shots back from the leader, Spain's Rafael Cabrera-Bello (63).