The experienced 44-year-old, in his third decade as a PGA Tour member, took advantage of benign morning conditions to compile six birdies and an eagle in a bogey-free journey around Waialae Country Club.
When he got to 8-under after 16 holes, he knew that finishing birdie-eagle would add up to 59, but he could only finish par-par.
Cook finished a mediocre 28th (fifth last) at last weeks Mercedes Championships, primarily, he claims, because of poor putting.
I was just blind on the greens, he said. I might as well have been putting left-handed, it was so pitiful.
This week I seem to have a better feel. Maybe I know these greens a little better. I have made some nice putts.
Despite his age, Cook is still strongly motivated to add to his 11 tour victories, which include the 1992 Hawaiian Open here at Waialae.
One of his motivations is because he wants to keep beating his 16-year-old son, Jason.
I worked pretty hard on my game this winter, he said. I have to keep sharp because my kid is going to start beating me if I dont. He already hits his irons further than mine.
Cook enjoyed a mini resurgence last year after two relatively barren seasons, winning the Reno Tahoe Open thanks to a closing 64.
His victim then was none other than Kelly, who led into the final round, only to blow up with a triple-bogey at the 16th hole and finish one stroke behind.
I did that to myself, said Kelly, still smarting at that loss.
Im not mister rosy outlook. I give myself a hard time.
Todays round was very similar to yesterdays. I started out shaky yesterday and I started out shaky today.
I was just feeling out my swing at the beginning. I didnt find it until the backside.
I found something on the (14th hole) and I was able to stick with it down the stretch. I really had some good chances.
Cooks 62 was matched by Charles Howell III, who come home in 29 strokes to move within six of the lead.
The cut fell at even-par 140. The most notable casualty was Davis Love III, whose 67 didnt quite compensate for his opening 75.
Mark O'Meara , who shot 68 Thursday, withdrew before the second round due to illness.
News and Notes from the Second Round
Full-field scores from the Sony Open in Hawaii