Three strokes off the pace overnight at Chambers Bay, Spieth picked up shots at the 10th, 14th, 15th - where he drained a 20-footer - and the 17th to get to six under in the season's second major.
However, he ran into trouble at the tricky 18th, which has been set up as a par four for the second round, after hitting his drive and third shot into bunkers before two-putting from 20 feet for a six.
That left the 21-year-old Spieth at four under for the tournament and one behind fellow American Dustin Johnson and Swede Henrik Stenson. Both scheduled to tee off in the afternoon.
Long-hitting Johnson and Stenson had set the first-round pace on the expansive links-style layout after opening with five-under 65s.
Level with Spieth at four under were South African Branden Grace, after nine holes, and Americans Patrick Reed, who was also among the late starters, and amateur Brian Campbell, after six holes.
The slick, undulating greens at Chambers Bay were heavily criticized by several players after the first round, mainly because of their uneven pace and bumpy nature due to the blotchy fescue grass.
World number two Spieth, however, has clearly adapted to the putting surfaces as he bids to become the sixth player to win the Masters and US Open in the same year, and the first since Tiger Woods in 2002.
While Spieth was mainly flourishing on a sunny day in the Pacific Northwest, where the US Open is being played for the first time, 14-times major champion Woods was at the opposite end of the leaderboard and destined to miss the cut.
A shadow of the player who dominated golf during the late 1990s and early 2000s, Woods was 11 over for the tournament after eight holes with just four players in the field of 156 faring worse.
Now shockingly ranked 195th, Woods struggled to an opening 80 on Thursday to record the fourth-worst score of his career as a professional and slipped further back after mixing two bogeys with a birdie.
Original source: Spieth one off early US Open lead