Furyk, meanwhile, posted an even-par 70. He and McDowell are knotted at 1-under 209 after 54 holes of the 112th U.S. Open at The Olympic Club.
Climbing into sole possession of third place at 1-over 211 was Fredrik Jacobson, who also carded a 68.
Matching the low round of the day with a 3-under 67 was third-ranked Lee Westwood, who ended the day in a fourth-place tie with two-time champion Ernie Els (68), Nicolas Colsaerts (71) and Blake Adams (70).
Second co-leader Tigers Woods, a three-time U.S. Open winner, stumbled Saturday. He fell to a 5-over 75, finishing the day in a tie for 14th place at 4-over-par 214.
Handler slams Piers Morgan: 'You're a terrible interviewer'
Ohio bar shooting arrested, charged with murder