Muyl tied it for the Red Bulls (1-0-1) on a close-range shot in the 51st minute and made it 2-1 with a volley off a defensive deflection in the 71st minute.
Bradley Wright-Phillips added a third goal for New York in the 85th minute and Daniel Royer capped the scoring in the 89th.
Cristian Espinoza opened the scoring in the fifth minute for San Jose (0-3-0) with his first MLS goal.
Matias Almeyda, who joined San Jose in the offseason after leading C.D. Guadalajara to a CONCACAF Champions League title in 2018, is still looking for his first point as coach of the Earthquakes.