Casey finished at 17-under 271, beating Miguel Angel Jimenez (68) and Peter Hanson (68). Defending champion Chris DiMarco (66) was fourth at 15-under.
"This was a great way to start 2007," Casey said. "I genuinely wanted to see if I could try to win one of the three out here in the Middle East. To win the first one was beyond my expectation."
Casey will play in the Qatar Masters next weekend and then the Dubai Desert Classic the following weekend.
"It's ecstatic to get better every single day and to finish it off with 65," said Casey, who started the tournament with a 71, then shot rounds of 68 and 67. "As far as professional rounds go, probably my finest final round."
Casey had five birdies on the front nine and three on the back, easily overcoming his three-stroke deficit from the third round despite a bogey on the last hole.
Jimenez, who was even with Casey after 16 holes, bogeyed the 17th after his approach landed in the rough near the green. The Spaniard needed to birdie the last to force a playoff, but he failed to hit the fairway with his drive and ended up with a par.
Padraig Harrington (71), Jean Francois (68) and Retief Goosen (68) tied for fifth at 14-under.
Shiv Kapur of India, in second place heading into the final round, ended with a 75 and finished tied for 20th at 279.