The 1934 FIFA World Cup was the first one that had a qualification process, as opposed to teams getting invited like 1930. As it is today, the qualifiers were regional and in North America Haiti faced Cuba in a preliminary round. After 3 matches, all played in Port-Au-Prince, Cuba came out victorious with 2 wins and a draw. In the final round of the region, the Cuban team would face Mexico but got eliminated with relative ease. Mexico then flew to Italy as they had qualified for the World Cup... or so it seemed.
Turns out that in the very last minute the United States registered to play the qualifiers, FIFA accepted their request and a last showdown against Mexico was scheduled. Because Mexico was already in Italy the match took place in Rome just 3 days before the start of the tournament. A crowed of approximately 12,000 people, including dictator Benito Mussolini, witnessed this playoff match.
The Americans fell behind 0-1 25 minutes into the first half, but ended up winning 4-2 at the end with a poker by Aldo "Buff" Donelli. A very frustrating turn of events for Mexico, who had flown to Italy to participate in the World Cup just to get knocked out in a surprise preliminary round against their biggest rival.
To ease the Mexican pain the United States were eliminated in the very first round against Italy, who would go on to be world champions, by a large margin of 7-1.
It is also worth mentioning that Donelli was an American Football coach at a college level, and only played soccer in local amateur teams. Those two matches were his only appearances for the USMNT, he then returned to the USA and went on to coach in the NFL.