Spieth is looking to become just the sixth man in history after Craig Wood, Ben Hogan, Arnold Palmer, Jack Nicklaus and Tiger Woods to win the Masters and U.S. Open in the same year.
The world number two can also became the first player since Gene Sarazen in 1922 to win multiple majors aged 21 or younger at Chambers Bay and cruised into the lead with four birdies in his first eight holes.
Starting on the back nine, Spieth birdied the 10th, 14th, 15th and 17th – he also three-putted the driveable 12th for par after missing from two feet – to reach six under par, one shot ahead of overnight leaders Henrik Stenson and Dustin Johnson.
However, the Ryder Cup star then hit the lip of a bunker with his second shot on the 18th, found more sand with his third shot and eventually carded a double-bogey six on the long par four, which had played as a par-five on Thursday.
Spieth was heard on television berating himself for the “dumbest hole I’ve ever played in my life” after his second shot, but bounced back immediately with a birdie on the first, which was playing as a 593-yard par five.
At five under par, Spieth shared the lead with Stenson, Johnson and fellow American Daniel Summerhays, who was putting together the round of the day with six birdies and one bogey in 15 holes.
South African Branden Grace and American Ben Martin were a shot behind, with Jamie Lovemark and JB Holmes setting the early clubhouse target on two under.
At the other end of the leaderboard, Woods was at least faring slightly better than he had during an opening 80, his worst ever score in the U.S. Open and his third round in the 80s in his last six events.
The former world number one pulled his second shot to the 10th – his opening hole – on to such a steep slope that he lost his balance attempting to take his stance, but recovered from the resulting bogey with a birdie on the 12th.
Dropped shots on the 14th and 18th were followed by a birdie on the first, but more bogeys on the second and third left Woods 13 over par, with just Lucas Glover and Ryder Cup captain Darren Clarke below him on the leaderboard.
Spieth three-putted from long range on the seventh but could be thankful for small mercies after seeing playing partner Justin Rose run up a triple-bogey seven.
Rose saw two approach shots fail to find the green and roll down a steep slope back towards him, although the first was the result of a complete mis-hit.
The 2013 U.S. Open winner then failed to get out of a bunker at the first attempt and eventually two-putted from 10 feet and, at three over par, was suddenly facing a battle to avoid missing the cut.
There were no such worries for Ryder Cup team-mate Lee Westwood, who carded an opening 73 but was four under par for his second round and just four off the lead at one under.