Ulsterman McDowell emerged from the shadows to win his first major at nearby Pebble Beach two years ago and the west coast was good to him again as he came in with a battling two-under 68.
Furyk, who won his first, and to date only major title, at the 2003 US Open at Olympia Fields near Chicago, had a level-par 70.
At one-under 209, they were the only men to duck under par on a pulsating day of quality golf, played on an unforgiving, but fair Olympic Club layout.
Two strokes back after a 68 for 211 came Swede Fredrik Jacobson, while England's Lee Westwood (67), two-time former champion Ernie Els of South Africa (68), big-hitting Belgian Nicolas Colsaerts (71) and US qualifier Blake Adams (70) were at two over.
Joint overnight leader and tournament favourite Tiger Woods had a nightmare round of 75 which left him at four over for the tournament with only an outside chance of ending his four-year long victory drought in majors.
Starting the day in a share of the lead on one-under 139, with Furyk and another American, David Toms, the former world No. 1 quickly fell victim to the opening six holes at The Olympic Club, which he rates as being one of the toughest stretches in major golf.
Woods bogeyed the first, third and sixth, and worse was to follow at the relatively easy par-three eighth where he three-putted to further plummet down the leader board.
It was starting to look bleak for the 36-year-old American, who is seeking his 15th major title, but he got a timely boost at the ninth when he sunk a 15-footer for birdie and a score of 37 at the turn.
But further bogeys down the back nine at the 16th and the last, where he badly fluffed a chip from stiff rough at the side of the green, left him shaking his head.
Toms went in the same direction by dropping five strokes in six holes and only Furyk held firm with two bogeys and a birdie to reach the turn in 35 and remain ahead at level par.
McDowell meanwhile played steadily with eight opening birdies before he bogeyed the ninth.
But showing the kind of determination he displayed at Pebble Beach, the Ulsterman dug deep for three birdies down the back nine.
The chasing pack was led by England's world No. 3 Westwood, who came in with a day's equal best score of three-under 67 to get to two over for the tournament.
Westwood has come agonisingly close in all four major tournaments over the last few years, and with the early exits of countryman Luke Donald and defending champion Rory McIlroy of Northern Ireland, he is the highest-ranking player left in the field.
"I'm really pleased. I gave myself a lot of birdie chances and a couple on 16 and 17 that would have made it a spectacular round," he said.
"I hit a lot more fairways and didn't really struggle, even the two bogeys I had chances to make par.
"I played a sensible, professional round. Major championships are good fun and it's nice to shoot a good round and be in with a chance tomorrow."
Els, a 42-year-old two-time former US Open champion, who has fallen on hard times of late, had an extraordinary round.
Starting the day at four over he looked to have played himself out of contention with three bogeys in the first five holes.
But he then bounced back, looking more like the Els of a few years back, with birdies at the seventh, eighth and 12th before chipping in for eagle at the 17th.
That gave him a two-under 68 and at two over for the tournament he ended the day with realistic hopes of a third US Open win an incredible 15 years after his last.
"Experience helps around here," was his verdict.
"For some reason I'm patient again this week and that's been kind of my virtue in Major Championship golf - the ability to be patient and wait it out.
"And I think you're going to have to do that tomorrow. If you have a little bit of a flyer somewhere in the round take it and then protect it."
Follow us @SprtNationalUAE