American Fred Couples made five birdies on his way to a final round of 68 and a share of third place.
Couples started the round at four under and wasted no time in making headway with a birdie at the first hole.
He followed that with another birdie at the fifth, but a bogey at the sixth put the brakes on his tentative charge.
Further birdies came at the ninth and 10th kept his scorecard ticking over, and his impressive day's play was rounded off with a birdie at the last.
Couples has finished in the top five of the Open on three occasions and in the top 10 eight times since making his debut at St Andrews in 1984.
He felt his final round this year could have been even better.
"I birdied the first, one lipped out on three, birdied five, close on seven. Number nine for eagle spun out. Then I birdied 10 and 18, and that was it.
"With a bit of luck I could've been a couple better off," he said ruefully.
John Daly, who won the Open in 1995, saw a promising start trail off for a round of 73, a five-under total and a tie of 15th place.
A birdie at the first raised hopes of a charge from the crowd favourite, but three bogeys saw off his chances of challenging.
"I had an opportunity to finish in the top 10 if I made any putts. I think I had 37 putts. If I had 32 putts, I finish in second place," he said.
World number four Phil Mickelson carded a disappointing round of 76 as he finished well off the pace at one over.
Mickelson had to wait until the 14th for his first birdie, by which time he had made five bogeys.
Mickelson's best form proved elusive at St Andrews
A bogey at the next hole summed up Mickelson's week, and a brilliant approach at the 18th for a birdie could not mask his out-of-sorts performance.
Meanwhile, five-time Open champion Tom Watson produced a round of 72 to finish the championship at one under.
The veteran American shrugged off a double bogey at the first to hit four birdies, but bogeys at the 12th and 17th brought his score back to par.
US Ryder Cup captain Tom Lehman's round of 70 contained six birdies and four bogeys to finish at four under.
Former champion Justin Leonard came up with his best round of the week, but it was too late to make any impact on the top end of the leaderboard.
His three-under-par 69 only featured one bogey and helped him to reach level par for the championship.