The 30-year-old journeyman had missed the cut at four straight majors heading into this year's championship at Erin Hills, and had arrived in Wisconsin with little expectation of victory.
After beginning the final round with a one-shot lead, the world No 50 looked to be edging closer to a fairytale win as he moved to the turn without dropping a shot.
But his hopes of victory evaporated when back-to-back bogeys, which coincided with a trio of Koepka birdies, left him with too much ground to make up.
"It bites a little bit right now," Harman remarked. "I had a couple get away from me yesterday. I was playing so good and just missed a couple putts."
