Federer and Zverev looked set to give Europe a commanding 10-5 lead in the match after taking two match points in the super tiebreaker at the United Center.
But a superb fightback from the American pairing saw them level before Isner then gave them a match point at 10-9.
A Sock forehand on the next point was then ballooned long by Federer to complete a dramatic win for the World team, who were mobbed by their watching team-mates following the victory.
"That was epic," world number 17 Sock said afterwards. "John makes my job easier. I played solid the whole match but made a few errors in the breaker.
"But John picked me up and carried me down the stretch."
The win gives the World an 8-7 lead with three singles rubbers to be played later Sunday.
With each rubber worth three points to the winner, two more wins for Europe or the World team will clinch the title.
World number two Federer was due to open the final round of singles matches, facing Isner. Federer holds a 5-2 advantage over Isner in head-to-head meetings.
In later games, Zverev will face South Africa's Kevin Anderson before Novak Djokovic takes on Nick Kyrgios in the final rubber of the three-day tournament.