Ryan Palmer, a West Texas native who cut through winds as strong as 25 miles per hour (40kph), had the round of the day with four-under 68.
Kevin Tway (69) and Tony Finau (69), the second-round co-leader this week, finished tied for third at 279, with Australia's Aaron Baddeley (68) fifth at 280.
After eight top-10 finishes since the start of past year, Chappell broke through on Sunday.
But after laying up at the par-five final hole, Chappell's measured wedge pitched on the back-left portion of the green and the putt for victory looked on target from the moment his ball left the clubface.
Koepka, who entered the tournament ranked 24th in the world, had five straight pars before a birdie on 18 to tie Chappell for the lead at 11 under.
Playing in his 180th tournament, the 30-year-old Californian holds a one-shot advantage over first-round leader Branden Grace (70), and John Huh (71).
"That was brutal", Grace said.
Chappell survives gusty winds to lead Texas Open by one
Chappell will have another golden opportunity to pick up the first PGA Tour win of his career, but there is no shortage of competition nipping at his heels. His day was relatively uneventful until the 14th when he got his first birdie of the round.
Cameron Smith during the Valero Texas Open. "I had played some really good rounds of golf". New Zealander Steven Alker, who was within a shot of the lead after a 67 in the first round on Thursday, had a nightmare round in the gusting winds on Saturday, shooting an 85. He made me had to do it the right way.
Koepka had to settle for outright second after piling the pressure on the leader, making birdies at the opening two holes and then three in a row from the sixth as he caught fire on the greens. That always tends to put me at ease.
Seamus Power and Graeme McDowell are both two over par after disapppointing rounds of 74 and 76 respectively. He also missed an eight-foot birdie putt on the drivable par-4 17th.
At Ridgedale, Missouri, Carlos Franco and Vijay Singh teamed to shoot a course-record 12-under par to rally from seven shots behind and win the PGA Tour Champions' Bass Pro Shops Legends of Golf at Big Cedar Lodge. He birdied three of his last five holes.
In all, 26 players are within five strokes of the lead heading into the final round, for which weather conditions are expected to mitigate.