Frost's bogey-free round left him at 14-under-par 130 at Hualalai Golf Club in the season opener of the Champions Tour.
With winds gusting to 28 mph, scores were higher in the second round, but it barely bothered the 53-year-old South African. Despite having his first-round lead cut in half, he remained in front with five birdies on the back nine, where he needed just 12 putts.
Cook, the 2011 Mitsubishi winner, holed out for eagle from 114 yards on No. 18 to finish at 6-under 66.
"We all have to pay attention," said Cook, who won in each of his first five years on this tour before being shut out in 2012. "It's early in the year. It's not like it used to be where you kind of played your way in the first couple weeks.
"You better come here with your game intact if you want to have a chance because everybody else is. These scores, for the first week of the year on a tough day like this, those are pretty good scores being shot."
Frost said the result of Cook's clutch final shot is "sometimes good, sometimes bad" going into the final day.
"Obviously the bigger lead you can have the better," Frost said. "With nine holes to go is where the action really starts tomorrow, so you just want to put yourself in position with nine holes to go. Sometimes with a big lead you guide yourself around the golf course. When you don't have a big lead you tend to play your natural game."
Two-time Mitsubishi champion Hale Irwin finished with a 68 to move into a tie for 11th.