The American posted nine-under-par round of 63 in Wisconsin, the lowest score in relation to par in the 122-year history of the US Open.
His 9-under tour of rain-softened Erin Hills eclipsed the 8-under-par 63 carded by Johnny Miller in winning the 1973 US Open at Oakmont, and matched the all-time low for any major of 63.
Below Harman on 12 under, three players are exhausted on 11 under - Thomas, Brooks Koepka and England's Tommy Fleetwood.
Fox is in its third year broadcasting the U.S. Open, having taken over from NBC's long-running coverage in 2015.
Rickie Fowler, on the verge of being left behind, rallied with three straight birdies and shot 68.
The US Open didn't seem to faze him, and he delivered a variety of big shots that led to his sensational finish. He still built a six-shot lead through 36 holes, despite hitting his tee shot into the ocean on the 18th hole and salvaging bogey.
Fleetwood, who was hoping to follow in the footsteps of 1970 victor Tony Jacklin and 2013 champion Justin Rose, held a share of second place on 11 under par alongside Americans Brooks Koepka and Justin Thomas.
However with strong winds ripping across the exposed, tree-less par-72 layout on Sunday, the odds on another low-scoring day lengthened. He dropped nine shots over the next seven holes three double bogeys, three bogeys and one par. "It's interesting to see where the USGA has gone with the U.S. Open, being a little more friendly than in years' past". Palmer shot a 65 after going into the final round trailing by seven shots. And yet, Thomas won't even walk to the first tee box Sunday with the lead.
Unusually, the finale will not feature any of the world's top three players.
Tom Kite knows a little something about hard conditions for the final round of the U.S. Open. The pressure of gaining that boost of confidence going into Sunday played a huge role during the third round. The final-round average was 77.2, and 20 players shot in the 80s. Kite says "I don't anticipate this being a bloodletting".
Justin Thomas was on fire in round three, shooting a nine-under 63 with the aid of nine birdies and a remarkable closing eagle set up by a three-wood to eight feet from 299 yards. The soft Black Course allowed players to take dead aim, and Barnes opened with rounds of 67 and 65.
But birdies will be harder to come by on Sunday with winds gusting from 25-30 miles per hour (40-48 kph), bending flag sticks and moving balls over hardening greens.
I hit good iron shots early on and good drives so I never really felt it was a struggle and didn't miss many shots. Spieth made birdies on the first two holes, both of which are playing downwind.
Then again, none of the top 16 on the leaderboard has ever won a major.