The Wildcats, fresh from winning last week's Pac-10 tournament, trailed the U.C.-Santa Barbara Gauchos, 35-32, at halftime.
Djokovic has played his best tennis when trailing at this tournament, saving four match points against Jo-Wilfried Tsonga in his quarterfinal.
The United States, which had never trailed in the tournament, fell behind, 2-0, before mounting a furious rally that was capped by Zach Parise's goal with 24.4 seconds remaining in regulation.
They have progressed from all four of their World Cup semi-finals and have never trailed at this tournament.
The South Americans, who are in France's Group E at the World Cup and face England in a friendly before the tournament, trailed to first-half goals from ex-Millwall midfielder Tim Cahill (2) and Crystal Palace's Mile Jedinak.
Eustachy and the ninth-seeded Golden Eagles were not far from extending their tournament run, trailing by as few as 3 points in the final minutes.
To the manager's credit his reaction was bold, flooding the box with attackers and, in the end, the two strikers introduced at the interval scored the goals to send the team to the top of Group B. England had never won a game at a major tournament having trailed at half-time.
Woods has never won a major tournament when trailing going into the final day.
But Gonzaga was far from stellar in its WCC tournament opener, trailing sub-.500 Santa Clara most of the way before pulling out a 77-75 victony on Stockton's layup with two seconds left.
Six-foot-6 sophomore Ruth Hamblin added 11 points and nine rebounds for the Beavers (23-9), who rolled through their first two games of the tournament without trailing for a single second.
