The U.S., which clinched a World Cup berth last month, didn't use most of its starters, and Gabriel Torres put Panama ahead in the 18th minute in a downpour at Panama City. Michael Orozco tied it the 64th minute, just as Costa Rica took a 2-1 lead at home against Mexico.
Luis Tejada scored in the 83rd, putting Panama within minutes of a fourth-place finish and a berth in next month's playoff against Oceania champion New Zealand. Mexico, which last missed the World Cup in 1990, would have been eliminated.
But Zusi scored 1:24 into three minutes of stoppage time, and Johannsson added his first international goal at the 2:40 mark to seal the U.S. win and Panama's elimination. The Americans, who have lost just once in their last 16 games, finished with a record-tying 22 points in the hexagonal, the final round of the North and Central American and Caribbean region.
It was a similar finish to four years ago, when Jonathan Bornstein's goal in the fifth minute of stoppage time gave the U.S. a 2-2 tie against Costa Rica, clinching a World Cup berth to Honduras and knocking out the Costa Ricans.
The U.S. (7-2-1) and Costa Rica (5-2-3) already had clinched berths last month, and Honduras (4-3-3) earned the region's final automatic spot with a 2-2 tie at last-place Jamaica (0-5-5).
Mexico (2-3-5) finished fourth with 11 points, three ahead of Panama (1-4-5), which has never played in soccer's top event. Before allowing the stoppage-time goals, Panama was even with El Tri on points and goal difference and would have advanced based on a 10-7 advantage in goals scored.
Having earned its seventh straight World Cup berth last month, the U.S. was without many of its regulars because of either injuries or decisions to allow them to return to their clubs. Among the missing were Landon Donovan, Clint Dempsey, Michael Bradley, Jermaine Jones, Tim Howard, Omar Gonzalez and Matt Besler.
In all, the Americans started just two players who began the clinching match against Mexico: defender Clarence Goodson and midfielder Alejandro Bedoya.
In the absence of Dempsey and Howard, Jozy Altidore captained the national team for the first time.
Torres scored after a giveaway by Edgar Castillo. Marcos Sanchez sent a layoff to the top of the penalty area, and Torres split the defenders and easily beat goalkeeper Brad Guzan with a one-timed shot to the corner.
Orozco scored his third international goal off a Davis corner kick. Sacha Kljestan was hauled down by Luis Henriquez right in front of the goal, allowing the ball to fall to Orozco. With his back toward the goal, Orozco lifted his left leg and made just enough contact to score from 6 yards. Orozco then did a little dance with DaMarcus Beasley, the American left back of late who was given the night off.
Panama could have been awarded a penalty kick two minutes later, but Jamaican referee Courtney Campbell didn't whistle Bedoya for knocking over Alberto Quintero as he streaked into the penalty area.
Two minutes later, Guzan got his left hand up to stop a point-blank shot by Torres.
Panama came back when Torres sent the ball down the right flank to Roberto Chen, who sent a low cross through the penalty area. Guzan slapped the ball with his right hand and the ball ricocheted to Tejada, who stepped in front of Kyle Beckerman.
But it wasn't over. Castillo started the set up to the tying goal with a pass to Davis, who sent the ball to Zusi, He climbed over Henriquez and his 8-yard header beat goalkeeper Jaime Penedo. It was his third international goal, and second in five days.
With Panama pressing to get the goal it needed to regain a tie, Terrence Boyd set up Johannsson for a goal on a 20-yard shot.
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