Spain's Jose Maria Olazabal was unable to exert the necessary pressure on eventual winner Tiger Woods as he carded a 74 to finish at eight under.
Olazabal, paired with Woods for the final round, cut the gap to one with a birdie at the fourth before a bogey at the sixth stopped his attempted charge.
As Woods cruised clear, Olazabal made four bogeys on the back nine.
Early challenges from the likes of Retief Goosen, Vijay Singh and Sergio Garcia all fell by the wayside.
Olazabal believes catching Woods is almost impossible after finishing tied for third.
The 39-year-old, who only qualified as a late reserve after Seve Ballesteros pulled out, was six shots behind the champion.
"I don't think it's impossible to catch Tiger but it's close to impossible. He played really solidly, was straight off the tee and controlled the distance."
"I'm a bit disappointed that I didn't play like I wanted but the week has been very positive for me," he said.
Goosen, starting three shots behind Woods, had a nightmare start to his round with four bogeys in the first eight holes.
Birdies at the ninth, 14th and 18th all came long after the horse had bolted.
Garcia suffered similar problems in getting his round going, with a bogey at the second knocking his confidence.
Sunday's final round did not go to plan for Garcia
A birdie at the fifth got him back on an even keel, but a double bogey at the 12th - swiftly followed by a bogey at the 13th - blew any chance the Spaniard may have had.
Michael Campbell followed up his US Open victory with a fifth place at the Open after a closing round of 72.
Meanwhile, Singh also went round in 72 to finish at seven under.
The former world number one had, at times, looked the most likely to mount a challenge to Tiger Woods, before a run of back-nine bogeys undermined his hopes.
Bernhard Langer had threatened to mount a serious challenge before also falling victim to the back nine.
Langer hit a brilliant eagle at the fifth and a birdie at the ninth, but any lingering hopes were dashed at the 15th with an embarrassing double bogey as a misjudged chip landed in the bunker.
Langer paid a heavy price for mistakes on the back nine
An error at the 17th was punished by a bogey, but Langer deserved the applause for the final-hole birdie that gave him a seven-under finish.
Australia's Geoff Ogilvy also reached seven under after a round of 69.
Lower down the leaderboard, Ernie Els hit a final round of 70 to draw the curtain on his disappointing Open campaign, finishing at two under and a tie for 34th.
Els' inconsistency was encapsulated by his birdie at the first and bogey at the second and, despite belatedly found some form with five birdies in six holes, two late bogeys spoiled his day.
KJ Choi's hopes of a high finish fell apart when he ran up a quintuple bogey at the treacherous Road Hole to finish with a 73 and a one-under total.
Choi's approach on the 455-yard 17th stopped on the road behind the green.
After failing twice to get up the back, frustration got the better of him and he thumped his fifth shot across the green into the Road Hole bunker.
He needed two more shots to escape and two putts added up to a nine, the joint worse score on the hole this week.