Kohles overtook Pendrith with birdies on holes 16 and 17 to take a one-shot lead, then bogeyed the 18th after hitting his second shot into greenside rough.
After having to chip twice from the rough and already looking stunned, Kohles missed a six-foot putt that would have forced a playoff.
"I wasn't really paying attention to what they were doing, although it really mattered, obviously," Pendrith said.
"I feel for Ben. He played really, really good today, especially down the stretch.
"I've been on the other side of it a couple times, and it sucks. But it's golf. It's a hard game."
Pendrith two-putted for birdie on the 18th, holing a three-footer for a four-under 67, leaving him at 23-under 261 at the TPC Craig Ranch.
On his 74th PGA Tour event start, the 32-year-old had won his first title.
Born in nearby Dallas, Kohles shot 66 to finish a stroke back. He remains winless on the tour.
"I did so many good things this week," Kohles said.
"I'm just going to keep reminding myself of that and try to get myself back in this position."
Sweden's Alex Noren, also seeking a first PGA Tour victory, was another stroke back.
He wowed the crowd on the stadium hole at the par-3 17th with a tee shot to 2.5 feet, but followed that birdie with a par knowing he probably needed an eagle on 18.
Noren shot 65 and was alone in third at 21 under.
Aaron Rai (64) and first-round leader Matt Wallace (68) of England were at 20 under along with the South Korean pair of S.H. Kim (64) and Byeong Hun An (65).
Pendrith, the third-round leader, and Kohles were separated by just one shot or tied most of the day.
After Kohles made a 20-footer to take the lead on 17, Pendrith's par putt rolled all the way around the cup and went in.
Jake Knapp, the second-round leader who three years ago was working as a security guard in his home state of California, shot 70 to finish at 19 under.
Min Woo Lee led the Australian charge, a final-round 69 leaving him in a tie for 24th at 15 under, while Adam Scott (68) was a shot further back in joint 30th.
Kris Kim, a 16-year old amateur making his PGA Tour debut, had a rough finish as the youngest to play a final round on tour in 10 years.
The son of South Korean-born former LPGA Tour player Ji-Hyun Suh had four bogeys on his back nine and shot 73 to finish six under.
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