Bieler broke a scoreless tie with his first goal in the 41st minute after Zusi found him with a pass outside the penalty area.
He doubled Kansas City's advantage in the 57th minute and Zusi made it 3-0 with his own tally 8 minutes later.
C.J. Sapong capped the scoring for SKC (5-3-2), which regained a share of the Eastern Conference lead with Montreal and New York.
Chivas USA, meanwhile, fell to 3-4-2, extending its winless streak to four games.