Lee led by two approaching the final three holes at Royal Selangor Golf Club in Kuala Lumpur but the South Korean double-bogeyed at the 16th and 18th.
That allowed Fraser to steal in and take the title with a flawless three under par 68 giving him a two-shot victory.
It is the Australian's third European Tour triumph and his first since lifting the Ballantine's Championship in April 2010, with the 37-year-old revealing he was spurred on to go all the way by his children.
He told the European Tour's official website: "It's unbelievable, six years since my last one. My kids keep saying to me every time I walk out the door, 'dad, can you bring home a trophy?' And I say, 'I'll try, I'll try'.
"This time I get to take one home and they can take it to school for show and tell, which is going to be pretty cool. That's the main reason I wanted to win."
Lee's round of 73 dropped him back to 13 under par overall and a tie for second place alongside Miguel Tabuena, with the 21-year-old Filipino matching Fraser's closing 68.
Nathan Holman of Australia settled for eighth, while Peter Uihlein's fantastic round of 66 was enough to lift him into a tie for ninth, with the American finishing alongside India's Rahil Gangjee and Japan's Masahiro Kawamura.
Louis Oosthuizen, the 2010 Open champion, equalled Uihlein's five under par round as he finished in a tie for 12th, while Danny Willett, winner of the Omega Dubai Desert Classic earlier this month, carded a disappointing 75 to finish in a share of 45th.