Chappell edged compatriot Brooks Koepka by a stroke with Americans Tony Finau and Kevin Tway sharing third on 279.
Chappell fired a four-under par 68 final round to finish 72 holes at San Antonio on 12-under par 276, edging compatriot Brooks Koepka by a stroke with Americans Tony Finau and Kevin Tway sharing third on 279.
Chappell, a six-time PGA runner-up, was seventh at the Masters two weeks ago.
"I'm just excited I don't have to answer the question, 'What do I have to do to win?' again," Chappell said. "There's a lot of excitement, frustration and joy right now."
Chappell found a bunker with his approach at the par-4 15th and missed a 13-foot par putt, taking a crucial bogey.
Koepka, who made seven birdies in the first 12 holes on his way to a final-round 65, sank a three-foot birdie putt at 18 to match Chappell for the lead.
But after Chappell missed birdie putts of 14 feet at the par-3 16th and 13 feet at the par-4 17th, he found the winning form on the final shot of the week.
"I was calm all day," Chappell said. "Never freaked out. It was simple. Make four and you win the golf tournament."
Chappell hopes the victory will launch him to a higher level, including consideration for this year's Presidents Cup and next year's Ryder Cup.
"Hopefully this is a platform to jump off of, to put myself in the conversation to make Ryders Cups and Presidents Cups and have my career really take off," Chappell said.
Chappell sank a five-foot birdie putt at the par-five second hole and followed with an eight-foot birdie at the par-3 third, but stumbled with a bogey at the par-4 fifth, missing a six-foot par putt.
He bounced back by putting his approach four feet from the cup and making the putt at the par-3 seventh, then began the back nine with a tap-in birdie.
Another tap-in birdie at the par-5 14th put Chappell two strokes ahead, setting the stage for the closing drama.
Australia's Aaron Baddeley was fifth on 280 after a closing 68, with Aussie Cameron Smith, Americans Ryan Palmer and Brian Gay and South Korean Kang Sung-Hoon sharing sixth on 281.
American Jimmy Walker, last year's PGA Championship winner, finished on 283 to share 13th.