The victory was Haeggman's first since the 1997 Volvo Scandinavian Masters and his third on the European Tour. He is playing this season on a medical exemption after breaking his ankle in an ice hockey accident.
'I tripped over and sat on my ankle,' said Haeggman, who broke his ankle in two places. 'I am not so fast these days and the bone didn't hold. I spent a long time trying to walk again but it's fine now. The nearest I get to an ice rink is 400 yards away when I drive past.'
Sato, an overnight co-leader, needed an eagle on the final hole of regulation to force a playoff but only made birdie. He carded a 4-under 68 on Sunday to post his highest finish on the European Tour.
Raphael Jacquelin, the other co-leader with Sato after the third round, managed a 3-under 69 and tied for third place with Brian Davis and Jose Manuel Lara, who both shot rounds of 5-under 67. The trio came in at 14-under-par 274.
Haeggman, who began the final round two strokes behind the co-leaders, broke out quickly on Sunday with five birdies in his first seven holes. He took over sole possession of first place with a tap-in birdie at the par-5 10th to reach 15-under par.
The Swede birdied the par-3 13th to go two ahead but dropped a stroke to par at the very next hole. Haeggman parred holes 15-17 to remain one up on the field as he played the par-5 18th at Doha Golf Club.
Haeggman sank a 15-footer for birdie at the last to go two in front of Sato and Jacquelin, who both needed eagle at the final hole to force a playoff.
Sato landed in the fairway at 18 but realized he could not make the putting surface in two. He laid up then pitched his third to six feet and made the birdie putt to go to 15 under.
Jacquelin tried a driver off the fairway with his second at 18 and landed in a greenside bunker. His blast did not fall into the cup and he made par to stay in third place.
With the victory, Haeggman now has his sights set on making this year's Ryder Cup team, a team he has made only once in 1993. He was one of Sam Torrance's advisors at the European victory in 2002 but now the Swede wants to be a bigger part of the action this September.
'The hard practice has paid off and I would love to get back into the Ryder Cup Team again,' said Haeggman, who went 1-1 at the Belfry in '93. 'I enjoyed walking the fairways with Sam last time, but I couldn't see why I wasn't there playing. This is just one step on the road and I feel I can cope with pressure and play at the highest level again.'
For Sato, this finish was a step in an ongoing process. Sato, who turned 34 on Friday, earned his tour card this year through Q-School but with his second-place check this week, he moved to 18th on the Order of Merit and looks to be in solid shape for retaining his card next year.
'I am so happy,' said Sato. 'I never expected to play so well and to make only two bogeys all week was good. I am pleased with the birdie at the last because I have done so much to keep my card for next year.'
Martin Maritz shot a final-round 67 and took sixth at 13-under-par 275, Greg Owen finished a stroke back at minus-12 thanks to a 5-under 67 in Sunday's final round.
Roger Chapman (70), Robert-Jan Derksen (65), Stephen Gallacher (67) and David Howell (70) shared eighth place at 11-under-par 277.
Darren Fichardt, the 2003 champion, shot a 1-over 73 on Sunday and tied for 36th place at 5-under-par 283.