He's joined at 6 under by second round co-leaders Bud Cauley (74) and Tony Finau (74), Sweden's Carl Pettersson (71), 2013 Texas Open champion Martin Laird (71), Kevin Tway (72) and Australian Cameron Smith (73).
Palmer, who graduated in 2000 with a degree in parks and recreation, shot a 1-under par, 71 Sunday after rounds of 74, 68 and 68 the previous three days.
Laird finished his day with a wonderful birdie on the par-five 18th hole.
Chappell struggled to a two-over start on the front nine, but he managed to salvage the round by birdieing three of four holes from No. 14 to No. 17.
Shot of the day: Chappell appeared to feel the nerves on No. 17 when he failed to convert a great birdie chance, but he steeled them on the final hole when he rolled in the winning putt from just over 8 feet with Koepka warming up nearby on the range.
"I just didn't give up any shots out there", Grace said.
But Koepka came up one stroke short as Chappell, in his 180th start on tour, finally found out what it felt like to win.
He had three bogeys, a double bogey and three birdies on the outward nine, which led to a two-over 38. This golf course really gets all of your game.
Former Texas A&M golfer Ryan Palmer captured his best finish of the season at the Valero Texas Open Sunday, finishing in a tie for sixth after carding a seven-under par for the week. It's nice for Kevin to get his first win. He made me had to do it the right way.
"I don't know what the weather has got in store for us tomorrow, but if it's a good day it's going to probably take a couple under (to win)", Grace said. 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. South Korean Kim Seung-hyuk shot a 69 and tied for third place at 10 under 274 with overnight leader Hwang Jung-gon and Japan's Mikumu Horikawa.
CHAMPIONS: Fred Funk and Jeff Sluman teamed to shoot a course-record 10 under to take the opening-round lead in the Legends of Golf in Ridgedale, Mo.
Sunday is set up for a frenetic finish with 26 players now within five shots of the lead.
Wiesberger has been in impressive form the last eight months, having not missed a cut since the PGA Championship with seven top-five finishes.