Cook, 53, is seeking his fifth victory on the Champions Tour. He got off to a good start, saving par from off the green at the 18th to grab the lead by himself.
Bernhard Langer, who leads the season-long points race for the Charles Schwab Cup, was among those in a tie for fifth at 67. Fred Couples, the only player who still has a chance to catch Langer in the points race, shot 69.
Langer and Couples were paired together and both had a spectacular shot during their opening round.
Langer made a hole-in-one at the par-3 third and Couples holed out from the fairway for an eagle at the par-5 10th.
Cook's round was highlighted by four straight birdies beginning at the ninth. He is trying to become the first player on the Champions Tour all year to successfully defend a title.