Mickelson and Bradley completed a 4&3 win over Australian Jason Day and Canada's Graham DeLaet in the top match and soon after South African Ernie Els and Zimbabwean Brendon de Jonge triumphed by the same margin against Bill Haas and Hunter Mahan.
That put the United States ahead by 4-1/2 points to 3-1/2 overall in their bid to win the trophy for an eighth time in the biennial team competition, and they led in two of the four remaining matches while trailing in two.
However, those were the only two encounters to finish at Muirfield Village Golf Club on Friday following a weather delay earlier of just over two-and-a-half hours due to a thunderstorm.
Play will resume at 7.35 am local on Saturday in what could be a marathon day, with five fourball matches and five more foursomes also on the schedule, though further thunderstorms have been forecast.
"It's going to be a long weekend, that's for sure," said Masters champion Adam Scott who, in partnership with Japan's Hideki Matsuyama, was four up on Zach Johnson and Jason Dufner after 11 holes. "Time to go rest up."
Steve Stricker and 20-year-old rookie Jordan Spieth were three up on South Africans Branden Grace and Richard Sterne after 14 holes while Tiger Woods and Matt Kuchar were three up on South Africans Louis Oosthuizen and Charl Schwartzel after 12 in the day's marquee match.
"We are playing well, both of us are playing well," said Woods. "I hit a couple of loose iron shots this afternoon, but made a couple good putts and we just kind of put the heat on these guys.
"Seven under (par) through 11 (holes), that's not bad in alternate shot. It's just one of those days where both teams are really playing well, but we still got our work cut out for us tomorrow."
The Internationals, who have lost the last seven sessions of foursomes played at the Presidents Cup, had welcome blue numbers on the leaderboard in the fourth and last matches out.
Argentina's Angel Cabrera and Australian Marc Leishman were one up on Webb Simpson and Brandt Snedeker after 13 holes while Scott and Matsuyama were firmly in control against Johnson and Dufner, having gone three up after just six holes.
Mickelson and Bradley had earlier staged a stirring comeback for the United States in the first match out before torrential rain swept across the course and, as thunder rumbled overhead, the siren sounded at 3:09 p.m. to halt the action.
The two Americans did well to go just one down after being outplayed by Day and DeLaet over the first four holes, then won the fifth, sixth, seventh and eighth to go three up.
Left-hander Mickelson sparked the fightback by sinking a 15-foot eagle putt from the fringe at the par-five fifth before hitting a stunning approach to inside two feet at the par-four sixth in the alternate-shot format.
Though the American duo stumbled late in the round, losing the 13th and 14th with successive bogeys after going six up with six to play, they sealed victory when Bradley sank a three-foot birdie putt at the par-five 15th.
"I felt like the par putt Keegan made on four was just a critical one," said Mickelson. "We were going to go two down and he makes a 15, 18-footer for par and gave us this momentum boost.
"That really started our streak because on five is where we got hot."
The United States, who have won the last four Presidents Cups, led by 3-1/2 points to 2-1/2 after Thursday's opening fourball matches when play was also interrupted by a thunderstorm.
(US pairs first)
Phil Mickelson/Keegan Bradley beat Jason Day (Australia)/Graham DeLaet (Canada) 4&3
Bill Haas/Hunter Mahan lost to Ernie Els (South Africa)/Brendon de Jonge (Zimbabwe) 4&3
Steve Stricker/Jordan Spieth three up on Branden Grace (South Africa)/Richard Sterne (South Africa) after 14 holes
Webb Simpson/Brandt Snedeker one down to Angel Cabrera (Argentina)/Marc Leishman (Australia) after 13 holes
Matt Kuchar/Tiger Woods three up on Louis Oosthuizen (South Africa)/Charl Schwartzel (South Africa) after 12 holes
Zach Johnson/Jason Dufner four down to Adam Scott (Australia)/Hideki Matsuyama (Japan) after 11 holes