Spieth sank an eight-foot birdie putt on his final hole, the par-three ninth, to set the early pace before being caught at the top late in the day by fellow American Patrick Reed, who three-putted the final hole for 69 in the more difficult afternoon conditions.
While former world number one Tiger Woods missed only his sixth cut at a major after battling to a six-over 76, Spieth fired a 67 after watching Jason Day, with whom he played, collapse because of dizziness off the ninth green.
“He (Day) was fine, he didn't say much (in the scorer's hut,” Spieth told reporters after a round that included six birdies, a bogey and a double at the tricky par-four 18th.
“He just signed his card and we told him to get some rest and water and whatnot.”
Spieth, aiming to become the sixth player to win the Masters and U.S. Open in the same year and the first since Woods in 2002, posted a five-under total of 135 in the season's second major, being played for the first time in the Pacific Northwest.
Fellow American Dustin Johnson (71), co-leader overnight with Swede Henrik Stenson, and South African Branden Grace (67) trailed by one shot.
Stenson slipped to equal 12th at one under after struggling to a 73 on the challenging links-style layout that became firmer, slicker and bumpier as the day unfolded.
Australian Day, who has been troubled by dizziness in the past, finished at two under after battling to a 70 before being taken to hospital where he was diagnosed to have suffered from Benign Positional Vertigo.
Spieth, a double winner on the 2014-15 PGA Tour, was delighted to end his round with a birdie after the unusual delay on the ninth green where Day was attended by four medics.
“That was one of the better birdies I've ever made given all the situation,” said the 21-year-old American. “Obviously there was some wait time in between, but I actually got somewhat of a read off Jason's putt and was able to knock it in.
“I struck the ball significantly better today with my approach shots. I hit my irons and wedges better today than yesterday, I also putted better today.
“I'm not quite putting myself in the same positions off the tee, so I've got to be a little more methodical. But if you shoot in the sixties at a U.S. Open you're going to be pleased.”
While Spieth mainly flourished on a hot day with gentle breezes, 14-times major champion Woods was at the opposite end of the leaderboard as he missed the cut at a U.S. Open for a second time.
A shadow of the player who dominated golf during the late 1990s and early 2000s, Woods slumped to a 16-over total of 156, his highest ever after 36 holes as a professional on the PGA Tour.
“I hit a little bit better today, but again I made nothing (on the greens),” said Woods, who struggled to an opening 80 on Thursday.
“I didn't make any putts the first two days; I hit it better today, hitting some spots where I could hit some putts; I made nothing.”
Northern Ireland's world number one Rory McIlroy fell nine strokes behind after dropping three shots in the final two holes, while defending champion Martin Kaymer of Germany missed the cut. – Reuters
Original source: Spieth shares US Open lead