'I feel fabulous and really happy that my perseverance has paid off,' said Cevaer. 'I am happy to have clinched one of the first opportunities that I have had.'
Overnight leader David Park stumbled to a 2-over 72. He shared second place at 8-under-par 272 with Peter Hedblom (70) and Ricardo Gonzalez (71), who was looking to win for the second straight week. Bradley Dredge and Jarmo Sandelin finished one stroke further back at minus-7.
Cevaer began the final round two strokes behind Park, who struggled early. Cevaer got off to a fast start as he holed a wedge from 137 yards out for eagle at the par-4 first. However, he tripped to a bogey at the very next hole.
The 34-year-old bounced right back with a birdie at the third and got to minus-11 with a birdie at the fifth. Things took a turn for the worse from there as he battled the breezy conditions at Fuerteventura Golf Club.
Cevaer faltered to his second bogey of the day at the seventh. He dropped another stroke at the 10th to fall to 9 under.
His struggles continued as he bogeyed back-to-back holes from the 12th to slide back to minus-7. However, Cevaer took advantage of the short par-4 16th. He pitched in for eagle from 53 yards out to jump into the lead at minus-9 and he parred the final two holes to cling to his first place.
'It has been a long time but I wanted him to enjoy watching me and feel the rewards for everything that he did, not only money that he put in but also the belief he had in me,' said Cevaer of his father.
Gonzalez, who was looking to become the first European Tour player to win back-to-back events since Vijay Singh won the Carlsberg Malaysian Open and Caltex Singapore Masters in February of 2001, got off to good start with a birdie at the third.
The Argentine stumbled to a bogey at the next hole but dropped in back-to-back birdies from the fifth to move to 11 under. He looked to be in control of the event as he rolled off five straight pars.
Gonzalez then faltered to a bogey at the 12th, but he remained in first place. He parred three straight holes, but the turning point came at the 16th. He knocked his tee shot out of bounds, which led to a double bogey that sent him tumbling out of the lead. He parred the final two holes to share second place.
'Finishing second is not bad, especially after last week, but it was just one bad shot which cost me, the shot went wrong because I wasn't thinking straight but that is the way it goes sometimes,' admitted Gonzalez of his shot on 16.
Park, who was looking for his second tour title, bogeyed the first but erased that mistake with a birdie at the very next hole. Things went downhill from there for the Welshman as he double bogeyed the par-3 fourth.
He stumbled to three straight bogeys from the sixth to slide all the way back to minus-5. Park thought he grounded his club in a bunker at the sixth, which would have led to a penalty, but was later told no such penalty was coming.
'If I have one regret, I should have asked right there and then what the penalty was because I played a couple of holes thinking I had incurred a penalty before discussing it with Chief Referee John Paramor on the seventh tee who told me I hadn't,' said Park. 'It didn't prey on my mind too badly, but I just felt a little silly really because I have been playing this game for a long time and you should know what to do but it was a spur of the moment thing.'
Park fought back with a birdie at the 10th. He nearly forced a playoff as he birdied Nos. 16 and 17. Needing a birdie at the last to force extra holes, Park only managed a par at the last for his share second place.
Hedblom had two bogeys and a birdie over his front nine. Around the turn, he picked up his second birdie at the 12th. He posted another bogey at 14, but came back to birdie the 16th. Like Gonzalez and Park, his playing partners, Hedblom had a chance to force extra holes by birdieing the last, but he could only par the hole.
Miles Tunnicliff closed with a 3-under 67 to grab a share of seventh place at 6-under-par 274. He was joined there by Charl Schwartzel (68) and Jose Manuel Lara (68). Marcus Fraser finished one shot further back at minus-5 after a closing 70.