Chasing his first major title, halfway leader Fowler looked set to maintain his overnight advantage until three-putting the 18th, the resulting level-par 70 leaving him on 10 under par.
Playing partner Clark hitting a stunning approach to the last to set up a closing birdie and complete a hard-fought 69, with McIlroy also recording a 69 as he bids to claim a fifth major and first since the 2014 US PGA.
World number one Scottie Scheffler finished eagle, birdie to card a second consecutive 68 and lie three shots off the lead.
McIlroy held a share of the lead after two-putting the first for a birdie and then holing from 12 feet for another on the third, but that proved to be the longest putt the world number three holed all day.
“I feel pretty good,” McIlroy said. “The golf course definitely got a little trickier than the first couple of days.
“I felt like I played smart solid golf. It felt somewhat stress-free, if you can ever call golf at a US Open stress-free, but overall pretty pleased with how today went. I feel like I’m in a good spot going into tomorrow.”
Quote of the day
Defending champion Matt Fitzpatrick was one of a number of players to note the subdued atmosphere.
Shot of the day
Minutes after Rickie Fowler holed from 70 feet for birdie on the 13th, Scheffler outdid him with a stunning eagle from 196 yards on the 17th.
Round of the day
Tom Kim began the day 11 shots off the lead but ended it in the top 10 thanks to a 66 which included a record-equalling front nine of 29.
Statistic of the day
Bad news for anyone hoping to stage a final-round charge from more than four shots off the lead.
The par-five eighth hole played to an average of 4.450, with three players making an eagle and 33 making birdie. There were just three bogeys.
The fifth hole proved the hardest with just one player making a birdie and three making double bogeys, leading to a scoring average of 4.510.
A cloudy start will give way to afternoon sun and highs in the mid 70s, with wind gusting up to 18mph in late afternoon.
Key tee times (all BST)
2157 Ryutaro Nagano, Xander Schauffele2208 Dustin Johnson, Harris English2219 Scottie Scheffler, Rory McIlroy2230 Rickie Fowler, Wyndham Clark