Yura Movsisyan scored twice for Kansas City, playing in place of Eddie Johnston, who is with the U.S. team at the CONCACAF Gold Cup.
Angel put the Red Bulls on the scoreboard first -- and became the first player to score eight goals in his first seven MLS matches -- when he took a pass from Dave van den Bergh and headed it into the net six minutes into the contest.
New York scored again when Clint Mathis got his fifth goal of the season.
The Wizards scored with two minutes left in the first half when Kerry Zavagnin scored his second goal of the year.
Kansas City tied the game on Movsisyan's goal in the 70th minute, and went ahead, 3-2, on Moysisyan's second goal in the 79th minute.