Positioned on the far post, Johnson took a nice pass from substitute Alan Gordon and headed the ball past goalkeeper Molvin James for the winner.
The Americans appeared to be heading to a surprising draw with win-less Antigua before Johnson's heroics at the Sir Vivian Richards Stadium in St. John's.
The result moves the USA to top of their qualifying group, three points ahead of Guatemala and Jamaica, who play later Friday. The USA have one more game in the semi-final qualifying round on Tuesday.
Johnson scored his first goal in the 20th minute, heading home another accurate cross, this time from Graham Zusi.
Antigua tied it up just five minutes later with Pete 'Big Pete' Byers driving into the area on the right and then sending the ball to Dexter Blackstock, who was inside the six-yard box for an easy finish.
The Americans created few chances after halftime and Antigua nearly went in front in the final ten minutes as Byers curled a drive just wide of the right post.
Antiguan goalkeeper James then produced a good save on Michael Bradley's header to keep the match even.