Zusi provided a helper on Teal Bunbury's goal in the 13th minute, which gave Kansas City an early 1-0 lead.
Nick DeLeon notched an equalizer for United 10 minutes later on a long run and pass from Andy Najar.
But Zusi netted the decisive tally after picking up Kei Kamara's cross from the left side and slotting it home.
The victory lifted Kansas City (13-7-4) past New York and into sole possession of first place the Eastern Conference.
D.C. fell to 11-8-3 with the setback.