Former PGA champ Day was way off the pace after his opening round of 76 but demonstrated his enduring class with a battling three-under 67 on Friday to get back to three over for the tournament - hovering around the top-20 and well inside a cut mark projected to be at seven over.
Day's round was the second best among the early day-two starters but he was still eclipsed by Burns, who shot a five-under 65, which featured six birdies, one bogey and a key par save at his final hole - the ninth - to record the best round of the tournament.
It left him heading to the clubhouse on three under, just one off the overnight lead held by fellow American J.J.Spaun, who was among the later starters after his opening, bogey-free round of 66 on Thursday.
Day's round, which began at the 10th hole, was ignited by a terrific eagle at his third hole - the gigantic par-five 12th that measures 647 yards.
He struck his approach from 323 yards to 20 foot from the hole and sank the eagle putt. Two birdies quickly followed in the next five holes.
His biggest disappointment as he looked set to finish with a 66 after two more birdies on the homeward nine was his wayward drive at the ninth that led to an anti-climactic final bogey.
Burns, who shot a final-round 62 Sunday at the Canadian Open before losing in a play-off, also started his second round on the back nine and birdied 11, 13, 17 and 18.Â
He responded to his lone bogey at the first hole by putting his approach at the next hole to about six feet.
World No.1 Scottie Scheffler had five bogeys and four birdies in his 71, to be left at four over, but fellow luminaries Dustin Johnson (10 over) and Justin Thomas (12 over) will both miss the weekend.
Australian Marc Leishman, who had begun promisingly with a 71, suffered in his second round, shooting a 75, including a double-bogey six at the ninth hole, to sit at six over.
Five-time major winner Brooks Koepka, one of 14 LIV Golf players in the field, started his day two shots off the pace but dropped back after a 74 that featured eight bogeys.
A day after Patrick Reed recorded the fourth albatross in US Open annals, Frenchman Victor Perez made a hole-in-one at the par-three sixth, the second ever ace during a US Open at Oakmont.
But the demanding course was clearly getting to some of the players, with former champion Jon Rahm another left grumbling as he tumbled down the leaderboard after a 75 to sit on four over.
"Honestly, I'm too annoyed and too mad right now to think about any perspective," the Spaniard said.
"Very few rounds of golf I played in my life where I think I hit good putts and they didn't sniff the hole, so it's frustrating."
With agencies
