Joakim Haeggman, who won this year's Qatar Masters, fired a 6-under 66 and is tied for fourth place with Darren Clarke, who shot a third-round 70. The duo is knotted at 9-under-par 207.
Louis Oosthuizen carded a 1-under 71 and is alone in sixth at minus-8. Overnight leader Alex Cejka of Germany struggled to a 4-over 76 on Saturday and is seventh at 7-under-par 209.
Havret traded a birdie and a bogey over his first two holes on Saturday but drained a 35-foot eagle putt at the third. He mixed two bogeys and birdie on the rest of his front nine to make the turn at 1 under par.
The Frenchman, who won the 2001 Italian Open, sank a 15-footer for birdie at the 10th to jump into first place at 10 under par. He reached the green in two at the par-5 12th and two-putted from 50 feet for birdie, which maintained his one-shot edge.
Harrington matched Havret in first place but Havret reclaimed the lead. Havret drove into the rough at the 14th but knocked his approach to 3 feet and tapped in the birdie putt. He went two clear of Harrington at the 15th when he holed a 10-footer for birdie.
Havret dropped a shot to par at the par-3 16th when his tee ball landed 60 feet from the hole. He three-putted for the bogey and only held a one-stroke advantage over the 2003 winner.
Harrington ran into his own trouble at the par-5 17th. He missed the fairway then failed to advance his ball back into the fairway. Harrington took a bogey on the hole and fell two behind.
Havret parred the 17th then found the fairway off 18 tee, which was critical for the Frenchman. On Friday, Havret drove into the water and left the hole with a triple-bogey seven.
Saturday was a different story because Havret landed safely on the green in regulation. He was 65 feet short of the hole but lagged a beautiful putt to two feet. Havret calmly rolled home the par putt to take the 54-hole lead for the first time in his European Tour career.
'I was disappointed, of course, with that triple-bogey but as I said at the time, that's golf,' said Havret. 'Overall I had a good day and I'm quite happy. I tried to take it shot by shot. I did some good things and I did some bad things but I just tried to keep going.'
Harrington was only 1 under par until he reached the par-5 12th hole. He missed the green with his second shot but chipped in for eagle to get to 9 under par.
The Irishman hit a spectacular tee ball to the par-3 13th. It stopped a foot from the hole and Harrington tapped in for birdie and a share of the lead at minus-10.
While Havret extended his margin, Harrington tried to keep pace. He drained a 7-foot birdie putt at the 15th to tie Havret at 11-under par but the miscue at 17, cost Harrington.
The No. 8 player in the world had only 8 feet for birdie at the last but missed the putt that would have gotten him within one.
'I fell asleep over the tee shot on the 17th by losing concentration,' said Harrington, who posted a 4-under 68 on Saturday. 'Obviously the putt at the last would have saved the day, but, no, it didn't. I am not even thinking about tomorrow right now. I am thinking about my lunch rather than defending this title.'
Immelman held the lead with three front-nine birdies but only came in at even-par on the back side. He finished a 3-under 69 and is in position for his third victory on tour.
'The course has really shown its teeth after the first day,' said Immelman, who won back-to-back South African Airways Open titles starting last year. 'You've got a British Open feel with the wind and the cold and a U.S. Open feel with the greens and the rough. You are just trying to hang in there.'
Nick Price is alone in eighth place at 6 under par after a third-round 70.
Order of Merit leader Ernie Els (72), Thomas Bjorn (72), 2001 U.S. Open winner Retief Goosen (69), Anders Hansen (73), Soren Hansen (70), David Howell (75), Soren Kjeldsen (71), Stephen Scahill (74) and Marcel Siem (73) share ninth at minus-5.