Johnson became the first player in MLS history to score three times in two straight games.
He scored in the 46th, 59th, and 85th minutes, and goalkeeper Kevin Hartman made one save for the Wizards (6-2-1), who assumed the top spot in the Eastern Conference with the second win in their last three games.
Juan Pablo Angel gave New York a 1-0 lead in the eighth minute.
Kansas City plays its next game at New York June 16, while the Red Bulls travel to Toronto Wednesday night.
Celebrity Breakups and divorces of 2014 [PHOTOS]