Barnes led fellow-American Lucas Glover by one stroke and faced the possibility of 36 holes at Bethpage Black on Sunday as he was among 16 golfers yet to tee off for the third round when action was suspended due to flooded greens.
Holder Tiger Woods, who won the 2002 Open played at Bethpage, was 11 shots back after posting a second-round 69 and making par to start his third-round hole teeing off from 10.
Sixty players made the cut set at four-over-par 144 after the 156-man field finally finished the second round on Saturday afternoon due to a backlog caused by storms that washed out Thursday's first round after just three hours and 15 minutes.
Players were sent out in twosomes from the first and 10th tees for the third round, which officials hoped to resume at 0730 (1130 GMT) Sunday, although that could be delayed if expected overnight rain damages the already soggy course.
Soft conditions made for receptive greens, and players fired at pins on the long layout.
PGA Tour rookie Barnes, the 2002 U.S. amateur champion who had an opening 67 on Friday, came back Saturday to birdie three of the nine holes he had left in his second round to go eight under par in the rain-marred tournament.
His 132 total was one lower than the old U.S. Open mark shared by eventual winner Jim Furyk and Vijay Singh at Olympia Fields in 2003.
"It's pretty cool," Barnes, 28, said. "At the beginning of the week you didn't think that score was out there."
Glover, who led by one stroke when play was halted on Friday due to failing light, came back to birdie one of his five remaining holes to finish with 64 for 133.
"The greens are still holding mid-irons and long irons," Glover said. "It's still very soft. If you get it in the fairway there are birdies to be had."
Early Advantage
Canadian Mike Weir, the 2003 U.S. Masters winner who led after the first round, was on 134 after a 70.
Tied for fourth on 137 were Peter Hanson of Sweden (71), Japan's Azuma Yano (65) and American David Duval (70), the former world number one who has not won in eight years.
Britons Lee Westwood and Ross Fisher, Americans Todd Hamilton and Sean O'Hair, and Canadian Nick Taylor, whose second-round 65 tied the lowest U.S. Open round by an amateur, were knotted at 138 in share of seventh.
World number two Phil Mickelson was on 139 along with fellow-American Steve Stricker, who fired a second-round 66.
The leaderboard reflected a big advantage for the first round's late starters who played in dry conditions on Friday.
Stricker and Westwood were the only two from the other wave to stand among the top 16.
"We got the short end of the draw but you don't focus on that, don't get a bad attitude," Stricker said.
Woods, who was among the disadvantaged flight, will have to match the biggest 36-hole comeback ever in order to win his fourth U.S. Open and 15th major. Lou Graham came from 11 behind to win the 1975 edition at Medinah.
"I need some lower scores," Woods said. "If you don't have mud on your ball you can pretty much go after every flag."
