Simpson was in the clubhouse with a one-shot lead at 1-over 281 as third-round leader Furyk and Graeme McDowell each had a chance to force a playoff with a birdie on the 18th.
But Furyk ended up bogeying the final hole and McDowell settled for a par, making Simpson the fifth U.S. Open winner to come from behind at the San Francisco course for a victory.
McDowell ended with a round of 3-over 73, tying Michael Thompson (67) for second place at minus-1. Furyk (74) finished two back at 3-over 283.
Second-round co-leader Tiger Woods -- a two-time U.S. Open winner -- ended in a tie for 21st at plus-7 following a round of 3-over 73.