Pendrith shot 4-under 67 for a 23-under 261 total at the TPC Craig Ranch. The 32-year-old won in his 74th career PGA Tour start.
Playing just north of his birthplace of Dallas, Kohles shot 66 to finish a stroke back. The 34-year-old who plays out of North Carolina is winless in 68 starts.
"Honestly, hadn't seen any rough like that all week," said Kohles, who moved to North Carolina when he was 10. "Just needed a little bit more umph on it. Did so many good things this week, and I'm just going to keep reminding myself of that and try to get myself back in this position."
Alex Noren, a Swedish player 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 1/2 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.
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.
"It just curled in, that putt on the last second there, which was unreal just to give me a chance," said Pendrith, who set it up with a chip from an awkward stance with his heels hanging over the lip of a bunker, after saving par with another testy putt at the par-4 16th.
The victory qualified Pendrith for the PGA Championship in two weeks and next year's Masters. He's also in the next three $20 million US signature events, starting next week with the Wells Fargo championship. Kohles and Noren also played their way into Wells Fargo with their Nelson showings.
With Wells Fargo and the PGA coming in the next two weeks, just three of the top 30 in the world ranking were in the field.
Jordan Spieth, the highest at No. 20, missed the cut for just the second time in 12 appearances at his hometown event. Defending champion Jason Day (22nd) and Tom Kim (23rd) didn't contend, with Day finishing one shot behind Kim at 9 under.
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. Knapp and Wallace were the only players in the top eight with a previous PGA Tour win.
The start of the final round was pushed back 2 1/2 hours because of overnight rain, and pairings turned into threesomes going off both tees with the players allowed to lift, clean and place shots in the fairway.
Wallace appeared to start a charge by chipping in for birdie at 12, the toughest hole of the week, and getting another birdie at the par-4 13th. A three-putt bogey on the par-3 15th stalled him out.
Rafael Campos, a 13-year journeyman from Puerto Rico who has spent most of his career on satellite tours, birdied five of the first six holes starting on the back nine to make the turn at 29.
The 36-year-old cooled off on his second nine before making a 48-foot putt from off the green for eagle on the par-5 ninth for a 63 that put him at 18 under.
Taiga Semikawa, a 23-year-old from Japan playing on a sponsor exemption, also finished at 18 after a 64.
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.
Playing his final nine on the front, the son of South Korean-born former LPGA Tour player Ji-Hyun Suh had four bogeys and shot 73 to finish 6 under.
Kim, who is from England, played on a sponsor exemption from the South Korean company and tournament title sponsor CJ Group.
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