The Americans appeared on their way to what would have been an embarrassing and perhaps very costly draw with the decidedly underdog Antiguans, who had produced only one point in their three previous group games.
Johnson, however, nodded in a crossing pass from Alan Gordon to give the Americans a vital victory.
Twelve teams from the North American region have battled through round-robin competition in three groups this year and the top two teams from each group will then conduct a tournament next year. The three leading teams from those six will earn a spot in the World Cup.
With one game left in the current qualifying round, the United States and Guatemala are tied for first place with 10 points, three ahead of Jamaica. Guatemala defeated Jamaica Friday 1-0 and will meet the United States on Tuesday in Kansas City.
A tie or win for the Americans in that game will put them into the final qualifying tourney. The United States would also advance if Jamaica ties or loses in its Tuesday match against Antigua and Barbuda.
Canada inched closer to becoming one of the teams in the final qualifying tourney with a 3-0 victory over Cuba in Toronto. Only 11 Cuban players showed up for the game, creating speculation that the other five members of the squad had defected.
The North American games Friday concluded a long day of World Cup qualifying around the globe, during which Spain and Germany rolled to one-sided victories.
Spain, which was held to a lackluster 1-0 win over Georgia in Group I of European qualifying last month, scored a 4-0 victory over Belarus to move three points in front of France.
Germany crushed Ireland 6-1 and stayed three-points in front of Sweden in Group C. England remained in control of Group H with a 5-0 decision over San Marino and Russia edged Portugal 1-0 in a meeting of the frontrunners in Group F. Russia now leads Portugal by three points through three of the 10 games that will be played during the qualifying campaign.