Els outlasted 57th-seeded Craig Stadler 1-up. The South African will now face Sweden's Pierre Fulke, seeded 21st, who defeated American Brad Faxon in 19 holes at the Metropolitan Golf Club.
The other Final-Four match will pit Steve Stricker against Japan's Toru Taniguchi. Taniguchi bettered fellow Japanese standout Shigeki Maruyama 2-and-1, while Stricker defeated local favorite Nick O'Hern in 20 holes.
Els grabbed an early advantage on his American counterpart, but a pair of failed attempts to get out of bunkers at the fifth and sixth holes turned a 1-up lead into a 1-down deficit.
Els managed to win the eighth hole to pull All Square, and then spun back his approach shot on the par-4 12th to two feet. The win gave Els a 1-up lead, which he maintained entering the 17th.
At the penultimate hole of regulation, Els was forced to sink a 10-foot par putt to maintain his advantage. He did just that.
Then, in equally dramatic fashion, with Stadler inside him, the Big Easy dropped in a 15-foot birdie at the 18th to win the match in the narrowest of margins.
'I kinda felt a little flat,' said Els, who defeated Jean Van de Velde over an emotional 19 holes in the Round of 16. 'I think both of us weren't really on our games. I just persevered.
'I know I've got another gear to put it into.'
Els will test that resolve against Fulke in Saturday afternoon's (Australian time) semi-finals.
Fulke overcame an early 2-down deficit to pull All Square through eight holes. The Swede looked to grab his first lead of the match at the ninth, until Faxon holed his greenside bunker shot for a halve.
One hole later, however, Fulke did take the lead after hitting his tee shot to within five feet of the hole.
Fulke then turned the tables on Faxon by holing his own bunker shot at the par-5 12th, this one for eagle. Fulke was now 2-up with six holes remaining.
Faxon won the 15th to move within 1-down, and then pulled All Square when Fulke found problems off the tee at the 17th.
After halving the 18th, Faxon appeared to have the advantage at the 19th hole, the par-4 14th. In the middle of the fairway, with a wedge in hand, Faxon flew the green and finished in the back bunker.
Fulke was short of the green in two, but putted from some 80 feet up to gimme range on his third shot. With a par secured, Fulke watched as Faxon blasted his bunker shot 20 feet past the pin, and then failed to convert a par of his own to extend the match.
'I started off pretty bad,' Fulke said. 'Once I got going I hit some pretty good shots. Hopefully, I can bring the good stuff into the afternoon round.'
Of the 34 Americans to make the trip to Melbourne, only Stricker remains. After defeating Justin Leonard 6-and-5 the day prior, the Wisconsin native struggled mightily against O'Hern on Saturday. Fortunately for Stricker, so too did the Australian.
Deadlocked through 18 holes, Sticker made a 12-foot birdie at the 19th hole, the 14th, to extend the match, and then stuck his approach shot at the 20th hole, the 15th, to three feet for the eventual victory. It was Stricker's only lead of the day.
'I struggled in the middle part of the round, but when I had to, I started to hit some good shots,' said Stricker.
Stricker will now face Taniguchi, who has yet to trail in any of his four matches thus far. The little-known Japanese player bettered his more famous countryman, Maruyama, in the quarterfinals.
Taniguchi was 4-up through seven holes, before Maruyama began to battle back on the back nine. Maruyama, who had never lost a match in Melbourne, going 5-0 in the 1998 Presidents Cup and 3-0 prior to facing Taniguchi in the Accenture, won the 10th, 13th and 14th holes to move within 1-down.
Maruyama appeared to be 20 feet from tying the match at the 16th, until his opponent rolled in a 50-foot birdie putt to ensure at least a halve of the hole. Maruyama then lipped out his birdie effort. Taniguchi had regained his 2-up lead, which he held onto for a 2-and-1 triumph.
Each of the four quarterfinal losers will receive $150,000. The winners are now guaranteed at least $300,000.
Following a brief rest, the four remaining survivors will square off in the semi-finals, Saturday afternoon.