The 27-year-old South African carded a closing 67 at Heritage Golf Club to set the clubhouse target at 16 under par.
That left Atwal needing an eagle on the par-5 closing hole for victory or a birdie to force a playoff, and the 44-year-old Indian gave himself a chance by hitting an excellent second from 20 feet.
However, his eagle putt lipped out, and on the first trip back down the 18th Atwal was unable to match Frittelli's birdie.
Frittelli was quick to pay tribute to his closest challenger after the tournament, telling Sky Sports Golf: "Arjun Atwal -- great payer, tremendous player.
"I played with him yesterday and it was one of the most fun rounds I've had in recent times.
"He's a player who's played all over the world, won in America, won all over the world and I'm glad I could steal one from him here.
"It's been a pretty good year for me. I've set some pretty lofty goals and achieved most of them so I can't wait for 2018 -- set more goals and go and chase them again."
A late charge from Louis Oosthuizen had earlier lit up the final round, with the former Open champion starting his back nine with a hat-trick of birdies and then hitting a spectacular second to the par-5 14th to set up his second eagle of the day.
However, his challenge ended as abruptly as it had began, with a wayward shot finding trees on the 16th and leading to a triple-bogey seven as he finished tied for seventh with a round of 67.