Triplett, who entered the day four shots off the pace, eagled the par-5 second hole, followed that with a birdie on No. 3 and was on his way.
He missed the green but nonetheless chipped in for a birdie at the par-4 16th, pushing his lead to three shots, and closed with a pair of pars to earn his first tour title.
Triplett finished at 10-under 206, two better than Mark McNulty, who posted a 3-under 69 to take second place at minus-8.
McNulty also was part of the winning Pro-Junior team with an amateur partner.
Second round co-leader Tom Kite stumbled to a 4-over 76 Sunday, ending in a tie for ninth at minus-4.