Stadler, who finished 168th on the PGA Tour money list this year to lose his tour card, had a 6-under 274 total on the Jockey Club course.
Cabrera finished with a 71. Scotland's Andrew McArthur (67) and Argentina's Rey Hernan (73) tied for third at even-par 280.
Craig Stadler, the winner's father and the 1992 champion, shot a 72 to tie for 18th at 7 over. The Stadlers are the only father-son winners in the history of the event.
'It makes me extremely happy to win such an important event. It's an event of great tradition and I'm delighted to join my dad in the winner's circle,' Kevin Stadler said. 'I felt the pressure all day. Maybe I didn't show it, but it was quite an struggle.'
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