The 29-year-old Griffin shot a one-over 71 to finish at 12-under 268 in the Charles Schwab Challenge, one stroke ahead of Schmid as both struggled through Sunday's round on a warm and windy day at Hogan's Alley.
Schmid (72), who took a four-shot lead into the final round, forced Griffin to make a four-foot par putt on the 72nd hole after his chip from the deep rough behind the green went in for birdie.
"I felt pretty good over it," Griffin said.
"It was just a left edge and trust it, let it slide in there."
Griffin and Schmid, the 27-year-old German seeking his first tour win in his 79th start, had matching scores each of the first three days in Fort Worth, Texas.
Schmid was the one who surged in front early in the third round, taking a three-shot lead. Griffin had a five-shot edge after just five holes in the final round, and finally let Schmid get within a stroke with a two-shot swing at 16 before getting the lead back to two with a hole to play.
Scottie Scheffler, the world No.1 and hometown favourite who won the PGA Championship last week, couldn't match his Saturday surge from 10 shots back. The three-time major winner began the day six shots adrift, but had two birdies and a bogey in a 69 to finish eight under.
Scheffler, who fell short of becoming the first to win three consecutive starts since Dustin Johnson eight years ago, tied for fourth, one shot behind Bud Cauley (67).
"Overall, three of the four days I played what I felt was pretty solid," Scheffler said.
"Just had one off day (on Friday), but outside of that, I did some good things this week as well."
Tommy Fleetwood (68) shot 31 on the front nine to get into contention, lost the momentum with a bogey at 11 and then had one of the tournament highlights with his final stroke.
A birdie putt on 18 stopped on the lip of the cup, and he waited almost 30 seconds hoping the gusting wind would push the ball into the hole. Nature obliged.
Australian Karl Vilips (70) finished in a tie for 11th at six under after three bogeys in his final eight holes.
Griffin teamed with Andrew Novak (71), who finished six under at Colonial, for the victory at the Zurich Classic in New Orleans last month.
With AAP & Reuters.
