The former US Open champion from Portrush picked up three birdies on the front nine to move into contention.
But his challenge faded with dropped shots at the 14th, 17th and 18th leaving him with a level-par 72.
McDowell finished on four under for the tournament and six shots behind winner Brian Harman.
Harman made a 28-foot birdie putt to win and end Dustin Johnson's hopes of winning a fourth title in his last four starts.
World number one Johnson, on his return from injury, shot a five-under 67 to set the clubhouse lead on nine under.
Ireland's Shane Lowry (72) ended on three under with Seamus Power (73) back on one over.
Graeme McDowell carded three late bogeys to finish in a tie for 18th at the Wells Fargo Championship in North Carolina on Sunday.