By Andrew Both
The 22-year-old Day was helped by Adams, who double-bogeyed the last after his second shot clipped a tree branch and ended in a water hazard.
"I wear my heart on my collar and I worked so hard to get to where I am today and this means a lot to me," Day told reporters after becoming the youngest Australian to win on the PGA Tour.
"I was disappointed that I hit it in the water and made it so hard on myself, but in the end I'm happy," said Day, the 2006 Australian amateur champion.
Day's first win took him longer than he expected but he said he had learned a lot.
"It was my own fault it didn't come sooner," he said. "I didn't practice hard enough the first year. You give someone a really good contract deal, everyone is telling you you're the best and it's easy to slack off.
"I've been working very hard this year and last year and it's finally starting to pay off, which is nice."
Day began the final round two strokes clear of Adams but slipped out of the lead after carding three bogeys in four holes just before the turn.
However, he birdied the 11th and 12th to regain a two-shot advantage and came to the last with a one-shot cushion.
Adams blamed a poor tee shot for his costly double-bogey.
"I was fortunate I had a wide-open (second) shot but I had some overhanging limbs and the ball was sitting on hard pan," he said.
"The ball shot up, hit a limb and threw it left, so I can't beat myself up over it. It leads back to that three-wood (tee shot). If I hit a good three-wood, it's a different story."
(Editing Peter Rutherford)