Starting from the tenth tee, world number 25 Spaun made four birdies before the turn and then parred his way home on a notoriously difficult course to reach a four under par 66.
That saw the early starter set a testing clubhouse target, and although he was briefly overtaken at the summit by Sungjae Im later in the day, no one was able to match or better Spaun's total.
South African four-time DP World Tour champion Thriston Lawrence sat alone in second on three under after carding six birdies in his 67, one ahead of Si Woo Kim, two-time former champion Brooks Koepka and Im in joint-third.
Spaun made an impressive start, holing his chip from a tricky spot in the rough at the tenth for an opening birdie before picking up his second shot of the day from close range on the 12th.
After sending his tee-shot to six feet at the par-three 16th to set up another birdie, Spaun holed a ten-footer on the next before parring the 18th to turn in 31 - the lowest first nine in a US Open at Oakmont.
And he made some wonderful par saves on his way in to keep his card clean.
Spaun was thrilled with his start to the week, saying: "I kind of came out here with no prior history at Oakmont, not really knowing what to expect even U.S. Open-wise. This is only my second one.
"I don't know if that freed me up in any aspect, but I just tried to kind of take what the course gave me.
"I hit a lot of good shots and tried to capitalise on any birdie opportunities, which aren't very many out here.
"But I scrambled really well too, which is a huge component to playing well at a US Open, let alone shooting a bogey-free round. I'm just overly pleased with how I started the tournament.
"It definitely makes me feel good, makes me feel confident that I'm leading the tournament. But there's plenty more golf left. This course is only going to get tougher."
Ten players were under par after 18 holes, with Jon Rahm, Thomas Detry, Rasmus Neergaard-Petersen, Ben Griffin and James Nicholas in a tie for sixth on one under.
Defending US Open champion Bryson DeChambeau carded a 3-over 73, tied with world number one Scottie Scheffler, while Masters champion Rory McIlroy managed to post 74.
Fresh off leading his Crushers GC squad to a third straight LIV Golf team victory, Bryson DeChambeau has doubled down on his belief that team-based competition is the key to golf's evolution.
JJ Spaun's incredible iron shots were backed up by a solid putting performance that led to his maiden major triumph at the US Open.
World number one Scottie Scheffler and Austin Eckroat share the lead after the opening round of the Travelers Championship on Thursday.
JJ Spaun called it "a storybook, fairytale ending" to his US Open win - and it's hard to argue.
