He, too, is looking for his first PGA Tour title although he has recorded six runners-up finishes.
He made a clutch par save at 17 after he drove to the front fringe and opted to putt, but he misjudged the line and pace and then raced his birdie putt four feet past the cup before the return dropped in the left side.
Beginning the day on two under par McDowell reached the turn on three under thanks to birdies on the 14th and 18th - his fifth and ninth holes.
"Obviously, the golf course hit me in the chin real hard early and I just couldn't find a rhythm, couldn't get a rhythm", Chappell explained.
NOTES: There have not been multiple leaders at the Valero Texas Open after 54 holes since 1993 when Jay Haas, Bob Lohr, Tom Lehman and Dan Forsman shared the lead at Oak Hills. Even though he lipped out the 11-foot eagle, his tap-in birdie gave him two strokes over Koepka. "After shooting 74 on Thursday, having to play good on Friday just to make the cut, and then to finish top six is huge". His scorecard included one birdie, five bogeys and two others - a triple bogey on the par-4 first hole (his round started on No. 10) and a nine on the par-3 third on which he hit three balls into the pond short of the green.
The win is the first on the PGA Tour Champions for Singh, and it's the second for Franco. He putted from 13 feet to save bogey.
Franco and Singh finished at 15 under in the rain-shortened 36-hole tournament, holding off a trio of teams that finished a stroke back.
Both Chappell and Grace had been trending in the right direction at the conclusion of the 2015-'16 season, but since have stalled, making the final round an important day for each of them.
Austrian Bernd Wiesberger beat England's Tommy Fleetwood in a playoff on Sunday to win the Shenzhen International in China.
Wiesberger went into the final round with a three-shot lead and eight shots ahead of Fleetwood, who closed with a 63 to catch Wiesberger at 16 under.
Among those who finished at 14 under were first-round leaders Jeff Sluman and Fred Funk, the winners of the tournament in 2014. His eight-foot birdie putt on 18 finally sealed it with a final round of 68.