Cook, who is seeking his second victory in three weeks, equaled the two-round tournament scoring record at 14-under 130. He made 10 birdies, so many he admitted he lost track during the round.
Watson shot a bogey-free 64 at the Sonoma Golf Club and Blackmar had a 67 to finish at 11-under 133.
Those tied for fourth at 135 were Russ Cochran, Brad Bryant and Jeff Sluman.
Cook finished his day with a spectacular shot from a fairway bunker to set up a birdie at the 18th.
"It really seriously was one of the best shots I've ever hit," Cook said. "It was really close to the edge of the bunker. I could have caught the lip and hit myself."
Loren Roberts, the Charles Schwab Cup points leader, struggled to a 73 and was in 25th place in the 29-man field.