A week after winning the Perth International on the European Tour, Van Pelt had an amazing 11 birdies in the first 17 holes and needed one more for a magical 59.
Instead the 37-year-old double-bogeyed for "only" a 62 and he will go into the final round alongside fellow American Robert Garrigus, who caught him on 16 under par with three closing birdies.
Tiger Woods still has five strokes to make up after a 69 that threatened to be so much better when he turned in a five under 30.
In a bizarre finish the 14-major champion bogeyed the 12th, birdied the next, double-bogeyed the short 14th, birdied the next, then dropped more shots at the following two holes.
Joint fifth at halfway, Woods fell back into a tie for 10th place.
Van Pelt was seven behind Garrigus after 36 holes, but resumed with two birdies and four more meant an outward 29. He then started for home with three more and when he added further birdies at the 16th and long 17th the opportunity to break 60 was there. But it was not to be.
Garrigus followed up his two opening 64s with a 69, while one behind is Chris Kirk after a 63 and two back are South African Jbe Kruger and Zimbabwe's Brendon de Jonge.