The South African Els became the fourth non-American champion in 29 years of the Memorial, joining Fijian Vijay Singh and Australians David Graham and Greg Norman as winners here. He also becomes the first player in event history to hold at least a share of the opening-round lead and go on to win the tournament.
'It was a tough week, but a very rewarding week,' said Els, who earned $945,000 for the win. 'My putter really saved me. Tiger (Woods) pushed us on the front nine. Then Freddie was pushing me. Luckily, I was able to make some big putts.'
Couples shot a final-round 68 to finish at 14-under-par 274. Woods, a three-time Memorial winner who at one point tied for the lead, ended with a 3-under 69 to finish at 12-under-par 276. Justin Rose was one stroke behind him at minus-11.
K.J. Choi struggled to an even-par 72 in the final round. He ended the event at 10-under-par 278, while Stephen Ames and 2003 Memorial winner Kenny Perry came in at minus-9.
Els opened the round with a two-stroke lead, but he dropped out of the lead with a bogey at the par-3 fourth. Couples chipped in for birdie at the same hole, his fifth chip in for birdie or eagle in the tournament, to jump to minus-12. He stood one shot ahead of Els.
Els, a two-time U.S. Open champion, came right back to birdie the fifth and join Couples in the lead. Couples and Els parred the fifth and were joined at 12 under by Woods, who birdied four, five and seven.
Woods, the World No. 1, could only par out, including a spectacular chip-in for par at the 14th at Muirfield Village. He had chipped in for par on the same hole en route to his win here in 1999. Woods went on to finish third for his third straight top-4 finish.
'I hit the ball very well this week,' said Woods, who won three straight Memorials from 1999. 'I'm playing better and this was another step in the right direction.'
Els regained the lead as he dropped in back-to-back birdies from the seventh and moved three clear of Couples with a birdie at the 10th. Couples fought back to within one shot of Els with consecutive birdies from No. 11.
Els stretched his lead back to two with a 30-foot birdie putt at the 13th. After making a stellar up-and-down par save at the 16th, Els closed the event in style.
The 2002 British Open champion birdied the 17th, as did Couples, to remain two clear of the field. Els then dropped his second shot within 5 feet of the hole at the last.
Els calmly rolled in the birdie putt for the four-shot win, as Couples bogeyed the final hole. With the win, Els joins Tom Watson and tournament host Jack Nicklaus as the only players to have won the British Open at Muirfield in Scotland and this event at Muirfield Village in Ohio.
'It means a lot. It's not quite like any other tournament,' said Els, who set a tournament record in needing just 100 putts to complete four rounds. 'It's got a little more prestige to it, especially with Jack Nicklaus as the host. And if you look at the winners roll, there's been quite a few great champions. I'm just so happy the way everything finished off.'
Couples, who won this event 1998, returned to the top 10 here after not playing last season and missing the cut in 2002.
'I was right there the whole time,' said Couples. 'That's a great feeling for me. I was second, but lost to the best player by far. He just turned it on on the back nine.'
Reigning British Open champion Ben Curtis closed with an even-par 72 to share eighth place at 6-under-par 282. He was joined there by Retief Goosen (71) and 50-year-old Jay Haas (71).
Rory Sabbatini, John Daly, Stephen Leaney, J.L. Lewis and Peter Lonard ended one shot behind that trio at minus-5.
Nicklaus rolled in a 10-foot par putt on the last to close with a 1-under 71. He shared 63rd place at 7-over-par 295.
'If I play again, then it won't make much difference, but if I don't play again I've shot under par the last tournament round I've played,' said Nicklaus, who has strongly hinted that his competitive playing days are over. 'I struggled with a few things, but basically played a pretty darn good round of golf. I had a chance to shoot a pretty darn low round, actually, and screwed it up a little bit, but still played all right.'