Mickelson and Bradley, going out first, lost the opening hole after International pairing Jason Day and Graham DeLaet recorded a birdie three, but then hit back in style by winning four consecutive holes from the fifth - all of them with birdies.
That put the American duo three up after eight and Mickelson could have increased that lead on the ninth but saw his birdie putt come up just short as the hole was halved. That group were on the 10th when heavy rain forced the teams off the course, with play being suspended due to the threat of lighting for the second successive day.
At that stage the US were up in three of the six matches as they sought to build on their one-point lead from the opening-day fourballs, with the International team leading in two.
Steve Stricker and Jordan Spieth were one up on Branden Grace and Richard Sterne after seven, although the South African pair had trailed by two before winning the sixth with a par.
Fred Couples' team were also one up in the fifth group to go out, where a birdie on the first from Tiger Woods and Matt Kuchar saw them narrowly ahead of another South African duo in major winners Louis Oosthuizen and Charl Schwartzel.
It was looking a little more promising for the visiting team in the second and sixth groups, however, where the pairings of Ernie Els and Brendon de Jonge, and Hideki Matsuyama and Adam Scott, were holding the upper hand with other matches square.