The triumph came in Kelly's 169th tour event.
Kelly never relinquished the lead he earned Saturday, shooting an even-par 70 as the chase group faltered. He also avenged a disappointing loss to Cook at last year's Reno-Tahoe Open.
A two-time runner-up in 200 career starts, Kelly finished the first full-field event of the season at 14-under 266 and earned the $720,000 top prize.
"It is burning me up inside right now," said the 35-year-old Kelly, who went to college on a hockey scholarship. "I'm not going to be able to sleep tonight."
Kelly made it a cheesehead weekend sweep. The Green Bay Packers defeated the San Francisco 49ers on Sunday in an NFL playoff game, one day after Wisconsin upset Michigan State in men's basketball.
"It was a sweep. I really put Brett Favre in my mind," Kelly said, referring to the Packers' quarterback.
Cook shot a 69 and settled for second at 267. He tied for the lead at 13-under with a birdie at the 18th, but could not overcome a bogey at the par-3 17th, where his backswing was affected by a ringing cell phone.
"I had a little miscue on 17 that I won't go into," said Cook, a 10-time winner on the PGA Tour who collected $432,000. "But we're happy for Jerry."