Watson, waiting for a maiden PGA Tour victory after more than 100 tournament starts, had a two-shot lead over Prugh heading to his final hole of the day at PGA West's Nicklaus course, one of four par-72s in use at the 90-hole pro-am.
A double bogey, however, gave Watson a three-under 69 and sent him into a tie for the lead with his fellow American at 23-under-par, Prugh, playing Silver Rock, having posted a 70.
South Africa's Tim Clark and American Bill Haas were a stroke behind after both players carded 66s at SilverRock and Nicklaus respectively, while Canada's Mike Weir shot a 67 at a Quinta to join Americans Matt Kuchar (65), Kevin Streelman (64) and Martin Flores (72) at 20-under-par.
Sweden's Richard S Johnson finished the day as the leading European after a 68 at SilverRock left him at 17-under with compatriot Carl Pettersson on 15-under following a 68 on the same course.
English duo Greg Owen and Brian Davis made the cut for the final round on nine-under but compatriot Justin Rose (eight-under) and Scotland's Martin Laird (five-under) both went out of the tournament.