Cook, 51, one of eight Champions Tour entrants in the tournament that features players from the four major tours, had 11 birdies and one bogey.
He played on the Del Monte Golf Course, one of three Monterey Peninsula courses used in the tournament.
I just kind of had it working, said Cook, who claimed his second career Champions Tour victory last month at the AT&T Championship. I really hit some quality shots and put the ball into good spots.
Cook, whose first of 11 PGA Tour victories occurred in the 1981 Bing Crosby National Pro-Am at Pebble Beach, played on the PGA Tour and Champions Tour in 2007 before joining the circuit for players age 50 and older this year.
Martin, 39, of Portland, Ore., a former assistant pro at the Olympic Club in San Francisco, had a bogey-free 65 on the Del Monte course, where eight of the top-10 first-round scores were posted.
Defending champion Tommy Armour III, one of eight former event titlists in the field, had an opening-round 66, also at Del Monte.
Former PGA Tour players Bubba Dickerson (Del Monte), the 2001 U.S. Amateur champion, and Brendon De Jonge (Spyglass Hill) trail Cook by five shots after shooting 67s. Dickerson and De Jonge both played on the Nationwide Tour in 2008.
Jill McGill and Janice Moodie led seven LPGA entrants after both shot 68s at Del Monte.
A Champions Tour player has never won the tournament. Juli Inkster, who edged Mark Brooks in 1990, is the only woman to win the event.
Rocco Mediate, runner-up in this years U.S. Open and winner of the 1999 Pebble Beach Invitational, withdrew for personal reasons after a 74 at Del Monte.
Following the 54-hole cut, the top 40 pros and 10 amateur teams will play the final round Sunday at Pebble Beach. The winner will earn $60,000.