Charles Howell III, David Berganio and Jerry Kelly share second place at 10-under-par. Two-time U.S. Open winner Lee Janzen, Jim Carter, first-round leader Brian Watts and Bryce Molder are two off the pace at minus-nine.
Cook's round was highlighted by an eagle-two at the par-4 12th hole, which played as the 31st toughest hole on the PGA Tour last year.
'I tapped in a seven-iron from 188 (yards),' quipped Cook about his eagle. 'It was a nice surprise.'
Cook added six birdies to his eagle in a bogey-free round at the Montreux Golf & Country Club.
'The course conditions were absolutely perfect,' said Cook, who has 10 career PGA Tour victories. 'It was a good striking day.'
Click Here for John Cooks' scorecard.
The 43-year-old Cook hasn't won since the 1998 Byron Nelson Classic and has just one top-10 finish this year -- a tie for fourth at Houston Open in April.
He'll have to fend off a bunch of younger players trying for their first win, including Howell and Molder.
Howell notched seven birdies and one bogey during a round of 66 on Friday. The 22-year-old former All-American from Oklahoma State has three top-10 finishes this year, including a playoff loss at the Greater Milwaukee Open.
'A win would mean everything,' said Howell. 'If I could win it would do a lot of things for me on the tour.'
Molder, meanwhile, is playing in his first tournament as a professional. The four-time All-American from Georgia Tech turned pro just this week after completing his amateur career at the Walker Cup. He opened with a 70 on Thursday and followed it up with a 7-under 65 on Friday.
'I came to try to win and I'm in a position with two rounds left to go to do so,' said Molder, who started on the back nine Friday and finished with five birdies on his last nine holes.
Berganio and Kelly, both trying for their first PGA Tour victory, each fired four-under 68s on Friday for their share of second place.
Watts followed up his opening-round 64 with a 1-under 71 on Friday, while Janzen carded a 7-under 65 on Friday. Janzen was at 10-under late in the round, but missed an eight-foot birdie putt on No. 17 and bogeyed the 18th.
Many of the top stars on the PGA Tour are at the NEC Invitational, an event that features an elite field based on appearances at the Ryder Cup or Presidents Cup.
Full-field scores from the Reno-Tahoe Open