The World Cup was Day's first tournament in five weeks and came less than two weeks after he learned that eight of his relatives, including his grandmother, died in the devastating Nov. 9 typhoon in the Philippines.
His mother, who immigrated to Australia from the Philippines 30 years ago, and sister were just off the green on 18 at Royal Melbourne. They both hugged him as he walked to the scoring tent to sign his card.
"It's just been an amazing tournament for me," Day said. "My mother, my family, coming down to support me. I'm just so happy the hard work has paid off, and I'm glad it happened in Melbourne.
"It would have been the easiest thing for me to just go ahead and pull out of the tournament with what has been going on over the last week," he added. "But I really wanted to come down here and play."
Day's situation wasn't lost on Bjorn.
"Obviously a fraction disappointed, I didn't play that great today," Bjorn said. "But I couldn't be happier for Jason winning. He has gone through a rough time of late and for him to even be here is a big thing and then to go and win a golf tournament ... that's what you want to see."
Masters champion Adam Scott finished third after a 66, three strokes behind.
Day earned $1.2 million for winning the individual title and helped Australia win the team portion of the World Cup. Day and Scott, who each holed approach shots for eagles Sunday, shared the $600,000 first-place team prize.
In Naples, Fla., Shanshan Feng of China seized control early and was flawless in the final round of the LPGA Tour season, closing with a 6-under 66 to win the LPGA Titleholders and claim the richest prize in women's golf. Feng opened with four birdies in six holes to go from two shots down to the outright lead, and she never gave it up the rest of the way at Tiburon Golf Club to earn a $700,000 check.
Gerina Piller stayed within one shot and had a 10-foot birdie attempt on the final hole that would have forced a playoff. It narrowly missed, and Piller had to settle for a 69 and her best finish on the LPGA Tour.
Pornanong Phatlum of Thailand had a 70 and finished alone in third.