Fowler had gone into the dramatic 11th at a rainy Scottsdale with his four-shot overnight lead intact.
However, when he attempted a straightforward pitch, his ball skidded through the green, narrowly missing a bunker before rolling into the water.
He took a drop and walked to the edge of the green to survey the shot, only to look back and see his ball roll back into the water.
Fowler was forced to take another drop – costing him a further shot – and, after leaving himself a testing putt, managed to hole it to a record a triple-bogey seven.
But it appeared to affect his focus as he also bogeyed the next, while Grace knocked in two birdies on the 12th and 13th holes to go into a one-shot lead.
Fowler birdied the 15th as both players were on 16 under heading down the final straight.
There was a two-shot swing in Fowler’s favour when Grace hit his drive into the water on 17, which led to a bogey five, while the American birdied the same hole, before a par on the 18th gave him victory.