'Chalk one up for the old boys,' said O'Meara, whose last win came at the 1998 British Open. 'It's been a big day for me, it really has. It's been a long time.'
Paul McGinley battled O'Meara throughout the final round and had a chance to force a playoff, but missed his eagle putt on 18. McGinley, who closed with a 2-under 70, ended at 16-under-par 272. A pair of former winners of this event, Ernie Els and David Howell, shared third place at 13-under-par 275.
World No. 1 Tiger Woods was trying to make one of his patented Sunday comebacks as he was 5 under through 10 holes. However, he stumbled to a pair of bogeys down the stretch to finish at 12-under-par 276.
O'Meara and McGinley, who played together all four rounds, began the day three strokes clear of the field. The duo each parred the first two holes to remain three ahead.
O'Meara dropped his third shot to the par-5 third at Emirates Golf Club within one foot of the cup to set up birdie. McGinley knocked his second greenside and left his pitch within inches of the hole and tapped in for birdie. O'Meara took the lead with a birdie at the next hole.
McGinley tried to keep up with a birdie at the fifth, but O'Meara answered with a birdie of his own to remain one ahead. The 47-year-old American fell back into a share of the lead as he bogeyed the sixth.
The Irishman McGinley lost his share of the lead for the final time at the ninth. His second shot out of the rough bounced into the greenside pond and led to a bogey.
O'Meara extended his lead to two strokes when he dropped his tee shot within three feet of the cup at the par-3 11th. He sank the birdie try, while McGinley two-putted for par.
McGinley, who shared second place here in 2000, clawed back within one stroke at the 13th. He knocked his third shot to the par-5 within eight feet and drained the birdie putt. The 37-year-old nearly joined O'Meara atop the leaderboard at the 15th, but his birdie try slid by the left edge.
O'Meara, meanwhile, was playing steady golf he two-putted five straight holes from the 12th.
McGinley lost any real chance to win or force a playoff when he bogeyed the 16th. He pulled his drive left into the trees and had to pitch out. He was unable save his par and fell two shots back.
O'Meara continued his steady putting. He again two-putted for par on 17 from about 18 out feet. At the par-5 closing hole, O'Meara laid up with his second shot, while McGinley pounded his second shot on to the green.
The 1998 Masters champion calmly dropped his third shot within 12 feet of the cup. McGinley needed to sink a big breaking eagle attempt from over 70 feet to try to force extra holes. The putt slid by the left edge and he tapped in for birdie.
O'Meara, whose new saw-like putting grip resembles the claw grip of Chris DiMarco, rolled his birdie try past the left edge and tapped in for par and the win.
Woods tried to make a big comeback on the final day. He started six shots behind the leaders and quickly picked up three birdies over his first five holes. He rolled in a 12-footer for eagle at the 10th to get to 13 under and within three shots of the leaders.
Things went downhill from there though. He flew green at No. 14 and had a poor stance in a bunker. He blasted across the green and was unable to save par.
Woods tried to drive the green at the short par-4 17th, but hit his drive through the dogleg and into the trees. He took an unplayable lie penalty, then knocked his third on the green. His lengthy par try came up inches short. Woods closed in fine fashion, though, with an up-and-down birdie at the last.
'I figured I needed to keep making birdies,' said Woods. 'I tried my best to do that, but I just couldn't do it.'
He was joined at minus-12 by Brian Davis (71), Thongchai Jaidee (67) and Marcel Siem (66). Joakim Haeggman, Peter Lawrie and Greg Owen shared ninth place at 11-under-par 277.