Palmer, locked in a duel with Robert Allenby to the very end at Waialae, came up short of the green on the par-5 18th and faced a delicate chip. Allenby went over the green and pitched to inside 10 feet.
Palmer thought his chip was a smidgen too hard, and he tumbled backward in relief when the ball struck the pin squarely. Allenby missed his birdie putt, and Palmer tapped in for 4-under 66 and his third career PGA Tour victory.
"Lucky bounce," Palmer said. "It was probably going to go by 7 or 8 feet. I still hit a good chip. You need things like that to win."
The victory gave made the 33-year-old Texan exempt on the PGA Tour through 2012, and earned him a trip back to the Masters Tournament for the first time in five years.
Allenby was trying to win his third consecutive tournament on three tours, a feat believed to have never been accomplished, and he gave himself every chance. He played bogey-free on the back nine, but he needed one more birdie. His second shot out of the rough on the 18th came out hot and over the green, and he did well to give himself a realistic chance at birdie and a playoff.
Steve Stricker, who also shared the lead briefly on the back nine, had 65 to finish third, two strokes back. Two-time U.S. Open champion Retief Goosen closed with 62 and was atop the leaderboard as Palmer and Allenby were making the turn.
Augusta native Charles Howell ended a stretch of 17 tournaments without a top 10 with a 66-64 weekend to tie for fifth with Carl Petterson (66) and Davis Love III, who holed out for eagle from the 16th fairway and closed with 67.