John Daly put himself into contention with a 6-under 66. The former major champion was joined by Steve Flesch in a tie for second at 9-under-par 135. Bo Van Pelt was one shot further back at 8-under-par 136.
Defending champion Tiger Woods flirted with the cut line on Friday but it was another big name who ended a streak.
Vijay Singh, the second-ranked player in the world, posted a 1-over 73 on the South course at Torrey Pines to snap a streak of 12 consecutive top-10 finishes in which he titled three times.
The missed cut was also the first for Singh since The Players Championship last March.
Woods started well on the North course, which rotates with the South course over the first two rounds. The world No. 1 birdied each of his first two holes but found trouble soon after.
He faltered with a bogey at the fourth and collected back-to-back bogeys from the sixth to fall back to even par, below the projected cut line at the time.
'I was off to a great start and then three bogeys right there in a row,' said Woods, who posted a 68 on Friday.
Woods recovered quickly, however, and dropped his second shot inside 15 feet for a birdie at the par-4 eighth. At the par-5 ninth, Woods played his third shot from the rough to three feet for another birdie.
The 28-year-old closed in fine fashion as well with a two-putt birdie at the par-5 14th. Woods then knocked his approach within four feet for a birdie at the 16th and added a birdie at the last to finish six shots off the lead in a group at 5-under-par 139.
'It's definitely reachable to win the tournament from there,' Woods said of his position. 'I don't have too many guys to pass. It's not too bad going over to the hardest golf course. It can be done.'
Cink dealt with the South course in the opening round and was faced with the North course on Friday, a layout that has yielded most of the low scores this week.
'Yesterday, I played at least as good as I did today, believe it or not,' said Cink, who posted a 70 in the opening round. 'Yesterday the fairways were hard, the greens were hard, and the pins were difficult.'
He started with two consecutive birdies from the second and landed his second shot inside eight feet for a birdie at the eighth. Cink then birdied the ninth and made it three straight with a birdie at the 10th after his approach stopped within three feet of the hole.
Cink made his surge up the leaderboard on the back nine with a birdie at the 14th. He added a birdie at the following hole and placed his second shot to 10 feet for a birdie at the par-4 16th to move to 10 under.
At the par-5 18th, Cink left himself with 25 feet for birdie and converted the putt to match his career best round on the PGA Tour.
'I stole one there,' said Cink, he previously shot a 63 in the final round of the 2000 NEC Invitational. 'It was a long bomb and it came at a great time.'
U.S. Ryder Cup captain Hal Sutton continued to play well with a second-round 70. Sutton joined Billy Mayfair, Stephen Leaney, Patrick Sheehan and Keiichiro Fukabori in a tie for fifth at 7-under-par 137.
First-round leader Kevin Stadler was one shot further back along with Sergio Garcia, Jesper Parnevik, Chris Riley, Luke Donald, Duffy Waldorf, Niclas Fasth, Dennis Paulson, Dean Wilson, Brandt Jobe and Brett Quigley at 6-under-par 138.
The 36-hole cut fell at 1-under-par 143 with three-time Buick Invitational champion Phil Mickelson surviving on the number.
'There's not much more I can do,' said Mickelson, who shot a 69. 'I had to birdie the last few holes to have a shot at it. Hopefully I'll play well tomorrow.'
Singh had a birdie opportunity at the ninth, his last, that would have sent him to the weekend but his putt failed to find the bottom of the cup.
Joining Singh in the group who missed the cut were Rich Beem, Mark O'Meara and Lee Westwood.