'I have shot 61 about four times in my career,' said Els. 'I've shot low numbers before but this is the first time in quite a while to have a go at breaking 60.'
Michael Campbell finished alone in second place at 8-under-par 64. Tobias Dier, who shot a 60 at the Dutch Open in 2002, was one shot further back along with Mahal Pearce, Craig Carmichael and Wade Ormsby at 7-under-par 65.
Els, who is trying to become the first person to win this event in three consecutive seasons, wasted little time in making history on the Composite Course at Royal Melbourne Golf Club.
He picked up his first birdie of the day at the par-5 second and followed that up with a birdie at the par-3 third after his tee shot stopped within 18 feet of the cup.
Els then dropped his approach inside eight feet for a birdie at the fifth and hit an 8-iron to four feet for a birdie at the next hole.
At the par-3 eighth, Els picked up another birdie to begin a remarkable stretch of golf that put him in a position to become the first person to shoot 59 on the European Tour.
'Over the last five, six, seven holes I really felt it. I wanted to break 60,' said Els. 'You don't get these chances too often. When it comes around, you try to go flat out.'
The South African roped a 3-iron to seven feet at the par-5 ninth and drained the putt for an eagle to reach 7-under. Els then grabbed a share of the lead with a birdie at the following hole.
Els kept cruising and birdied the next four holes to reach 12-under par on his round.
His magical run was derailed by a bogey at the par-4 15th but Els bounced right back with a birdie at the very next hole.
'The last nine holes I felt like I was playing the last day of a golf tournament,' said Els. 'You feel like you need to make more birdies to win the tournament. That's the kind of pressure I felt.'
Els had chances down the stretch but settled for pars on the closing holes to match the lowest 18-hole score on the European Tour.
'I can complain but I am not going to,' said Els, who established a course record at Royal Melbourne. 'I hit a lot of great shots and made a lot of good putts and had a lot of good fortune going my way. It was one of those special rounds.'
Campbell, who is a two-time winner of this event, collected eight birdies and no bogeys to set the pace early but in the end finished a distant second.
Adam Scott, who played alongside Els, joined fellow Australians Peter Fowler, Richard Green, Peter O'Malley and Paul Sheehan at 6-under-par 66.
Reigning U.S. Amateur champion Nick Flanagan, who played in the group with Els and Scott, posted a 5-under 67 to finish alongside Gary Evans, Peter Hanson, Peter Hedblom, Gareth Paddison, Craig Parry and Craig Spence.
Nick Faldo, who tied for second at this event last year, was one shot further back in a group at 4-under-par 68 that featured Ian Poulter and Paul Casey.