'It was a very tough day today, very hot,' said Choi's translator. 'It was just another one of the experiences that he feels makes the PGA Tour the best tour in the world.'
Choi on his win in New Orleans
Geoff Ogilvy and Dudley Hart shared second place at 14-under par.
Check out Choi's Scorecard
John Cook, Chris DiMarco, Mike Sposa and Dan Forsman shared fourth place at 13-under par. Nick Price finished alone in eighth at minus-11.
Several competitors threatened Choi's lead around the turn but Choi was nearly flawless down the stretch to fend off all contenders. Choi made the turn with a one-shot lead but a 30-foot birdie putt at No. 11 extended his lead to two.
Choi converted a three-foot birdie at 13 to go up by three and his approach at the 16th rolled to the lip of the cup with half of the ball dangling over the hole. The kick-in birdie gave him a four-stroke edge at 17-under par but perhaps his best shot had to yet to come.
He missed the green at the par-three 17th but chipped in for birdie from the rough 35 feet away.
Choi bogeyed the last hole when he missed a four-footer but by that point the tournament was locked up and so was the $810,000 first-place check.
'He feels very thrilled to have this tournament as his first PGA tournament win in his career,' said Choi's translator. 'He hopes that this will open up the doorways for the next generation of fellow Korean golfers to make the transfer over to the PGA Tour.'
Choi became the eighth first-time winner on the PGA Tour this season and continued an interesting trend on the PGA Tour. He became the sixth consecutive third-round leader who marched on to victory on tour. Vijay Singh started the pattern with his win at the Houston Open and Choi kept it going as he grabbed a one-shot lead after Saturday's third round.
Bryce Molder was one of the golfers who was in striking distance of first but he ran into serious putting problems on the 10th green. He four-putted the hole, with the last three inside four feet to seemingly fall out of contention with a triple-bogey.
The former Georgia Tech star gained entry into the tournament through a sponsor's exemption and fought back with three birdies on the back side but three closing bogeys dropped him into a share of ninth.
Molder posted a one-over 73 Sunday to come in at 10-under par. That score matched him with American Ryder Cuppers Phil Mickelson, Scott Verplank, defending champion David Toms and South African Tim Clark. More importantly, the top-10 finish gets him an invitation to next week's Byron Nelson Classic.
'I'm disappointed but it's a long process,' said Molder. 'This is just a small step. It could've been a bigger step. But I'm excited. I had a chance to win, I had a good time and I'm playing next week. Not too bad.'
Ogilvy and Hart each posted rounds of five-under 67 Sunday but neither mounted a serious charge to Choi's lead.
Full-field scores from the Compaq Classic of New Orleans