Jordan Spieth continued his serene progress around Royal Birkdale as he fired a flawless 65 to set the pace on 11 under, with Kuchar still in touch on eight under after a 66 despite a late double-bogey at the 16th during an enthralling battle between the top two.
But the battle between the Americans at the top of the leaderboard was overshadowed by the earlier exploits of Grace, who plotted his way faultlessly around the defenceless Southport links to etch his name into the major record books.
The South African cruised to the turn in 29 with five birdies, although his chances of breaking the 63 barrier looked slim when he parred the next four holes before he holed a superb 35-foot putt for birdie at 14.
He missed out on a birdie at the long 15th, but he rattled in another monster putt on the next green and two-putted the 17th to get to eight under, and he held his composure to get up and down from the rear fringe at the last.
That earned Grace the early clubhouse lead on four under, with world No 1 Dustin Johnson a shot further back after coming close to matching his feat, but he could not find the birdies he needed down the stretch and ended up slightly frustrated with “only” a 64.
But Grace’s score was never likely to hold up in the conditions as Spieth and Kuchar began to put daylight between themselves and the chasing pack, with Spieth forging ahead with an early birdie on the third before he holed from 10 feet for another at seven.
Kuchar birdied three of the first five holes but also bogeyed the fourth, and the final pair both made excellent threes on the eighth as they reached the turn in 31 before exchanging pars over the next four holes.
Spieth’s lead was then trimmed to one when Kuchar converted a solid tee shot at the short 14th, and they both birdied the next before Kuchar came to grief at the 16th, running up a double-bogey six which gifted his Ryder Cup team-mate a three-stroke advantage.
Kuchar clawed one back with a brilliant up-and-down from the sand for birdie at 17 which Spieth could not match from the same trap, and the pair provided a grandstand finish as Spieth holed from 20 feet for birdie at the last after Kuchar came close to holing his approach, but he was unable to convert the chance from six feet.
Branden Grace was unaware he was about to make major history at Royal Birkdale
Brooks Koepka put early pressure on the leaders with three straight birdies on the front nine, and he responded to a bogey at 13 with birdies at the two par fives before a poor drive at the last cost him another dropped shot as he settled for a 68 for five under alongside Austin Connelly.
The young Canadian made an astonishing start when he birdied the first and then holed his second for eagle at the next, and further birdies at the last two holes added up to a 66 which earned him a share of third with the US Open champion.
World No 2 Hideki Matsuyama cruised round in 66 to join Grace on four under, while defending champion Henrik Stenson believes he will need to better last year’s closing 63 to stand a chance of retaining his crown after he returned a six-birdie 65 to join Johnson, Chan Kim (67) and Rafa Cabrera Bello (67) on three under.
But Rory McIlroy’s chances of landing his first major since the 2014 PGA Championship look to be over after he paid the price for a number of careless mistakes following another bright start to his round.
McIlroy birdied the first for the second day running and picked up further shots at the fourth and fifth to get within two of the lead at the time, but lost ground with bogeys at seven and eight before reviving his hopes with a birdie at nine to turn in 32.
However, he pulled an iron off the tee into a fairway pot bunker and a poor splash-out left his ball on the lip of the next trap, from where he tugged his third into the greenside rough and took three more to get down.
He did manage to claw one shot back at the long 15th, but he could only par in from there as a 69 left him nine shots adrift of the leader on two under par alongside Richie Ramsay and English veterans Ian Poulter and Ross Fisher.