The Trinidad and Tobago-born golfer was cruising at two-under through 11 but dropped shots on the 15th, 16th and 17th to finish with a disappointing one-over 71.
At two-under, 208 overall, the 45-year-old is 15th on the leaderboard, nine strokes adrift of clubhouse leader Colombian Camilo Villegas who carded a 67 to remain out front at the PGA National Resort.
He is three strokes clear of Australia’s Nathan Green and Fiji’s Vijay Singh at eight-under with the American pair of George McNeill and Matt Every tied for fourth two strokes back.
Ames, who shot a course record 64 in Friday’s second round, started poorly with a double bogey on the first but birdies on the par-3 fifth and par-4 sixth, returned him to even par.
He picked up another shot on the ninth to make the turn at one-under and when he birdied the par-4 11th, it looked as if he would fire on the back nine as he had done a day earlier.
But after parring three straight, he followed that up with three dropped shots to fashion a messy end to his round.
