Ulsterman McDowell emerged from the shadows to win his first major at nearby Pebble Beach two years ago and the California 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.
The former world No 1 Tiger Woods struggled to a five over 75 that leaves him five strokes behind joint leaders Furyk and McDowell, and with 11 other players sandwiched in between.
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