SHEBOYGAN, Wis. — After a 314-yard drive on the par-5 16th hole at Whistling Straits, Jason Day had a decision to make.Ahead by three strokes in his bid to win his first major championship, Day could lay up with his next shot, which would have been the smart but conservative move, or go for the green as if he had nothing to lose.Day did not deliberate for long. In the previous two majors of the year, he had held at least a share of the 54-hole lead and had failed to win. Six times since 2013 he had posted top-10 finishes at golf's four biggest annual events.He was going to win the 97th PGA Championship on Sunday or go down swinging from his heels.Using his 4-iron, Day hit a dart that landed on the fringe of the green. He made a birdie to get to 20 under, and that was where he finished, closing with 5-under 67 for the day for a total of 268 on the par-72 layout to beat Jordan Spieth by three strokes.Day set a major championship record for strokes under par, beating by one the mark set at the 2000 British Open by Tiger Woods, whose success inspired Day, 27, to pursue golf as a career. As a teenager in his native Australia, Day read a biography about Woods that fanned the flames of his desire."It's a fantastic record to hold," Day said. "It's an amazing feeling I have."Woods, 39 and a 14-time major winner, missed the PGA cut, but he cast an ethereal shadow over the final pairing of Day and Spieth. While Day motored full speed ahead toward Woods' major scoring record, Spieth tried in vain to draft off his wake.After titles at the Masters and the U.S. Open, Spieth, 22, was trying to become the third man, and the first since Woods in 2000, to win three majors in the same year. He carded 68 to complete his 16 rounds at major tournaments in 54 under, the best season score in the modern era (since World War II), bettering Woods' 53 under in 2000.Spieth called Day's winning performance "a clinic to watch.""He was sitting there swinging as hard as he could off the tee," Spieth said.Day was in tears before he even tapped in for par on No. 18. He sobbed on the shoulder of Colin Swatton, his caddie and longtime coach, who rescued Day as a 12-year-old struggling to overcome the death of his father. "I didn't expect I was going to cry," Day said. "A lot of emotion has come out because I've been so close so many times and fallen short. To be able to play the way I did (Sunday), especially with Jordan in my group, I could tell that he was the favorite. Just to be able to finish the way I did was amazing."Day was soon joined on the green by wife Ellie and their 3-year-old son, Dash, for the celebration.Of all his near misses, Day said he gained the most from his tie for ninth at the U.S. Open in June. He played the last three rounds with vertigo. A few times he had to steel his will just to stop from walking off the course and quitting. By grinding out a tie for ninth, Day proved to himself that he had the fortitude to break through the ceiling of his comfort zone."It was good for me to understand how far I could really push myself and really understand that it's okay to go out there and just keep battling," he said.The hard-earned calluses that Day developed in his closing rounds at the U.S. Open and the British Open, where he tied for fourth with Spieth, helped him hold his position Sunday. He settled himself with a birdie on No. 2, the first of his four on the front nine (against one bogey). He made the turn with a four-stroke lead over Spieth and Justin Rose and a two-shot lead over Branden Grace, who was playing in the pairing directly ahead of him.All was not lost for Spieth, who supplanted Rory McIlroy, 26, as the world No. 1, ending McIlroy's 55-week reign.McIlroy shot 69 to finish 17th at 9-under 279 in his first tournament since rupturing a left ankle ligament last month. He has spent a total of 93 weeks as the world's top golfer.With the victory, Day moved to third in the rankings, meaning that golf's top three have an average age of 25."As long as I am healthy, I feel like I'm going to be there a long time," Day said. "I still want to accomplish that No. 1 goal of mine, which is to be the best player in the world. I'm still motivated and still very hungry for that, even after this win."Day lost his father to cancer when he was 12. If not for Swatton, he might have lost everything else.They became surrogate father and son soon after Day arrived at Kooralbyn International School, a 30-minute drive south of his hometown of Beaudesert, Australia, and where Swatton was the golf coach. Day's mother, desperate to get her son off the streets and away from a crowd of toughs who prized fighting and drinking, took on a second job to pay the tuition."It's pretty well documented that Jason could have been on the wrong side of the tracks when he was 12 and that's true," Swatton said. "He could easily have gone the other way."He would have wound up in a totally different spot. He wouldn't have been standing on the 18th green at Whistling Straits." The Associated Press contributed to this report.