Kjeldsen finished at 14-under 274 and won by three shots at Real Club de Golf de Sevilla.
'I've been so nervous all day,' admitted Kjeldsen. 'It was one of those days where conditions were different. It was tougher. I didn't feel all that happy about the way I was hitting the ball.'
The three-stroke margin of victory over David Drysdale, who shot a 2-over 74, was misleading. The pair was tied for the lead at 14 under par on the par-5 16th.
Kjeldsen hit his second into the water at 16 and appeared to be in trouble. Drysdale was dry, but missed the green with his third shot. Kjeldsen hit a spectacular fourth to 15 feet, while Drysdale's birdie chip ran 8 feet past the stick.
Kjeldsen sank the tough par save and Drysdale converted his shorter par save and the two remained tied.
At the par-3 17th, Drysdale blocked his tee ball into the right bunker. Kjeldsen played a strong shot to 20 feet, then watched Drysdale chunk his blast from the sand. Drysdale was still away and missed his 25-foot par save.
Kjeldsen rolled home his birdie effort and the two-shot swing left him two clear with one to play.
The Dane hammered his drive down the fairway at the last and Drysdale landed in a bunker. Drysdale pulled his approach into the water guarding the putting surface.
Kjeldsen played it safe with his second and stopped the ball 20 feet from the hole. Drysdale dropped and nearly hit his fourth into the water. He got up and down from the side of the green for a double-bogey.
Kjeldsen took a very aggressive line with his birdie putt and ran it almost 10 feet past. He missed that putt, but the bogey hardly mattered thanks to Drysdale's miscues at 18.
Kjeldsen visited the winner's circle for the third time on the European Tour. His previous victories came at the 2003 Diageo Championship at Gleneagles and last year's Volvo Masters.
'The first time I felt comfortable was after making the putt on 16 actually,' acknowledged Kjeldsen, who netted four birdies and four bogeys on Sunday . 'For some reason, that settled me down a bit. I needed to make a few good putts, which I did.'
For Drysdale, this runner-up finish was his best on the European Tour. He was one-under par through 16 holes and had a great chance to get his first victory.
Colin Montgomerie, the European Ryder Cup captain, celebrated his 500th European Tour appearance this week. On Sunday, he posted a 2-over 74 and finished in a tie for 31st at even-par 288.