The US trailed by a point following Thursday's opening foursomes but won three of the five better-ball matches to leave both sides on 5-1/2 points going into the afternoon foursomes.
US Open champion Furyk and PGA Tour veteran Haas, fired by nine birdies in 11 holes, set the tone by hammering Australians Stuart Appleby and Adam Scott 6 and 5 in overcast and damp conditions at the par-73 Links course.
The 49-year-old Haas, a captain's pick for the first Presidents Cup in 1994, holed a 30-foot birdie putt at the 494-yard fourth to launch his team's charge.
The American duo relentlessly tightened their grip until the win was sealed at the par-five 13th.
Kenny Perry and Davis Love III, in the second match out, beat Retief Goosen and K.J. Choi of South Korea 2 and 1 before Chris DiMarco and Justin Leonard picked up the third point with a one-hole victory over Fiji's Vijay Singh and Nick Price.
The Internationals, who fought back on day one after trailing in four of the six foursomes, grabbed their first fourballs win when Australia's Robert Allenby and Canadian Mike Weir beat Phil Mickelson and David Toms 3 and 1.
Mickelson and Toms, paired together for the second day in a row, had forged ahead by one with a birdie three at the sixth.
But Allenby and U.S. Masters champion Weir dovetailed well on the back nine, surging to victory with five birdies in nine holes.
The last match out had been billed as an effective head-to-head between world number Tiger Woods and local favourite Ernie Els, but it was little-known South African Tim Clark who underpinned a crushing 5 and 3 win for the Internationals.
"It was great to watch," Els said of Clark's performance. "From my side, I think I helped him on just three holes. He really put Tiger and Charles (Howell III) under pressure from the start."
Presidents Cup rookie Clark, peppering the flags with radar-like accuracy, set up four birdies on the front nine to put the Internationals three ahead of Woods and Howell at the turn.
An out-of-sorts Woods secured his only birdie of the day at the par-five 13th, but the South African pair clinched victory at the par-four 15th, leaving the world number one winless in five Presidents Cup fourball matches.
Five foursomes will be played on Friday afternoon with six fourball matches to follow on Saturday. The trophy will then be decided over the closing 12 singles matches on Sunday.
