The 26-year-old Simpson, who triumphed twice on the PGA Tour last year, charged into contention with four birdies in five holes around the turn on the way to a two-under-par 68.
On a foggy afternoon at the brutally difficult Olympic Club, Simpson coolly parred his last eight holes to finish at one-over 281 as the other main contenders faded over the closing stretch.
Northern Irishman McDowell, winner of the US Open at Pebble Beach two years ago, closed with a six-bogey 73 to tie for second with little-known American Michael Thompson (67).
Furyk, US Open champion in 2003, was tied for the lead with three holes to play but bogeyed 16 and 18 for a 74 and a five-way share of fourth place at three over.
Three-time champion Tiger Woods, aiming to end a four-year major title drought, never recovered from a stumbling start and tied for 21st at seven over after returning a 73.
