Brain Harman has a one-shot lead at 12 under.
A three-time victor on the PGA Tour this season, Thomas also joined the exclusive "59" club by breaking 60 at the Sony Open, but he may have saved his best for Father's Day weekend and his quest for his first major crown.
Justin Thomas eagled 18 to get to 9-under 63, matching the major scoring record and breaking Johnny Miller's U.S. Open record for low round in relation to par.
Thomas may have had one of the more entertaining birdies of the afternoon at the par-4 fifth. One example of that was Fowler hitting 3-wood into the green on the 632-yard 18th hole, with a breeze at his back.
Fowler heads into the final round two off the pace, while one-time joint-leader Paul Casey slipped down the leaderboard after a triple-bogey at the fourth hole.
Joining Thomas in joint second place is countryman Brooks Koepka and England's Tommy Fleetwood (both 68).
Koepka is looking for his second win on tour, and first major, after the 2015 Waste Management Phoenix Open.
Fowler, who shared the 36-hole lead at the Masters in April, never came seriously close to bogey because he was never in trouble. The two-time European Tour victor is making just his eighth appearance in a major championship and is looking for a maiden PGA Tour win in his second US Open.
Thomas is one shot back at 11-under after a record-setting 9-under round of 63, the best score to par in a single round in U.S. Open history.
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World No.9 Rickie Fowler (68) is solo fifth, with Players Championship victor Si Woo Kim, from South Korea, a shot back in sixth after also carding a 68. "I'd like to shoot a good round here".
Players again took full advantage of a softened Erin Hills layout on Saturday, the course left defenceless by overnight rain and only a slight breeze.
"He loves golf. He actually wants a new driver or something, but I think we can find him something in the shop at the end of the day", Jonas said. "Whether that was two back, two up front or tied for the lead - let's go".
"I couldn't possibly shoot any higher than I did", Johnson said.
Johnson, ranked No. 1 in the world, missed the cut after a 1-over 73, which came a day after he shot 75. Here's a live look at the scores from Day 3. I just struggled on the greens.
On the longest course ever for a major, the cut was the lowest at the U.S. Open since 1990.
Fowler, the world number nine from California, revelled in benign conditions at Erin Hills Golf Course to reel off seven birdies and 11 pars in a superb 65.
There were 32 sub-par rounds, a record for U.S. Open third rounds.
Rory Mcilroy, of Ireland, and Jason Day, of Australia, walk on the eighth hole during the first round of the U.S. Open golf tournament Thursday, June 15, 2017, at Erin Hills in Erin, Wis. "We're definitely in good position for tomorrow". "You know every year I played the U.S. Open everyone complained Monday, Tuesday and Wednesday that his course is too hard".
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