Cook’s first PGA Tour victory came in the 1981 storm-plagued Bing Crosby National Pro-Am. The event was shortened to 54 holes due to the weather conditions. Cook won the title on the third extra hole after a five-way sudden-death playoff that included Hale Irwin, Bobby Clampett, Ben Crenshaw, and Barney Thompson. Hale Irwin, the last of the four men that Cook eliminated in the playoff, was gracious in defeat. Irwin said: “John is a special young man. He deserved to win. He is one of the best new young players on the tour.”
Cook’s second PGA Tour win came in the 1983 Canadian Open. Cook won the tournament with a birdie putt on the sixth extra hole of a playoff against Johnny Miller, after both players parred the first five extra holes.
At the 1990 Las Vegas Invitational, Cook lost a playoff to Bob Tway in memorable fashion. On the first hole of sudden-death, Cook hit a sand wedge shot into the hole from 95 yards for an apparent birdie only to see the ball bounce out of the hole and eventually finish 15 feet from the hole, but off the green. Tway won the playoff with a routine par.
In 1992, Cook won three PGA Tour events, including a two-shot victory at the United Airlines Hawaiian Open after shooting two closing rounds of 65. He moved into the top-10 of the Official World Golf Ranking for the first time that year.
Cook has had seven top-10 finishes in major championships. The closest he came to winning a major during his career was when he led the 1992 Open Championship at Muirfield by two shots late in the final round. Cook missed a two-foot birdie putt on the 17th that would have given him a three-shot lead before he bogeyed the 18th and lost the Open by one stroke to Nick Faldo. The Englishman birdied two of the last four holes to overtake Cook. After the tournament Cook said: “I definitely let one slip away. I had a chance to win a major championship and I didn’t.”
During three consecutive years between 1996 to 1998, Cook had at least one PGA Tour win. His 1996 victory in the FedEx St. Jude Classic came after his opening three rounds of 64-62-63 for a 54-hole score of 189 broke the lowest total in PGA Tour history for the first three rounds.
The last of Cook’s eleven PGA Tour wins came in the 2001 Reno-Tahoe Open at the age of 43.
He was inducted into the Ohio State Varsity O Hall of Fame in 1986.