New Zealand's Michael Campbell posted a 66 to finish alone in second place at 11-under-par 273. Overnight leader Eduardo Romero was one shot further back at 10-under-par 274.
Els quickly put the tournament out of reach with some exceptional play over the opening holes of the Alpine Course at Golf Club Crans-sur-Sierre.
The South African two-putted for a birdie at the par-5 first to pull within one of Romero and grabbed a share of the lead with a birdie at the second.
Els kept the run going at the par-3 third after his tee shot stopped 12 feet from the cup and he ran home the birdie putt to take sole possession of the lead.
At the par-4 fourth, Els dropped his approach inside 15 feet and drained the putt for his fourth consecutive birdie to start the round.
Els found trouble off the tee at the fifth but scrambled to reach the putting surface and converted a 20-foot putt to save par and keep the momentum alive. Els then hit his second shot to 15 feet for another birdie at the seventh to reach 16-under and pull four shots clear of the field.
'I made the perfect start today to do something special with four birdies but that was a career par at the fifth,' said Els. 'What a hole that was. But from being two behind and all of the sudden I was ahead and although I lost a bit of rhythm after my brilliant start, I felt like I kept everything together.'
He struggled on the green at the eight with a three-putt bogey and cooled down from that point on until a birdie at the par-5 15th after his second shot landed just off the putting surface.
The three-time major champion added a birdie at the 17th to complete the remarkable comeback win and increase his lead in the Order of Merit (European Tour money list) race.
'You can ask me about the Order of Merit after the American Express,' said Els, who leads Darren Clarke on the money list. 'Darren won a million bucks in the NEC Invitational and he's back into it and there are a lot of other guys playing well.'
Els, the second-ranked golfer in the world, put together a brilliant performance throughout the week. However, his six-stroke victory on Sunday was not the largest of his 2003 campaign. He won the Johnnie Walker Classic by 10 shots in February.
Romero, who was trying to become the oldest player to ever win a European Tour event, held a two-shot lead after 54 holes but could only move backwards on Sunday.
The Argentinean was overtaken by Els' early surge and made matters worse for himself with a bogey at the sixth. Romero then tallied back-to-back bogeys on the inward half for a final-round 74.
'I putted terrible,' said Romero, who is a two-time winner of this event. 'Nothing happened for me today. I tried my hardest to win but it wasn't to be.'
Robert Karlsson, who won this event in 2002, carded a 72 to finish in a tie for fourth. The Swede was joined by Scotland's Andrew Coltart and Emanuele Canonica of Italy at 9-under-par 275.
Sweden's Peter Hedblom finished one shot further back in seventh place alone at 8-under-par 276.
Paul Casey, Brian Davis, Paul Eales, David Howell, Miguel Angel Jimenez, David Lynn and Jarrod Moseley shared eighth place at 7-under-par 277.