With more than two years remaining before the World Cup is contested in Brazil, the Americans began their trek with a win in the rain that turned out to be more difficult than anticipated.
The Americans could not add to the advantage during the early stages of the second half and suddenly found themselves leading by just one goal when Peter Byers tallied for Antigua and Barbuda in the 64th minute.
An almost constant assault on the opposition goal, however, finally resulted in a score from Gomez.
The United States is in Group A during this round of qualifying along with Jamaica, Guatemala and Antigua and Barbuda.
The top two teams from each of the three four-team groups will then advance to the final stage of qualifying, which will be played next year.
Three teams from the six final countries will advance automatically to the World Cup and the fourth-place team will take on the second-place club from the Oceania region for a trip to Brazil.
The United States will play the second of its six Group A qualifying games next Tuesday in Guatemala City.