On the decisive play, Patrice Bernier got past a pair of defenders and sent a through-ball to Di Vaio, who slotted a shot behind Red Bulls goalkeeper Luis Robles.
The goal was enough to hand a fourth straight win to the Impact (4-0-0), who lead the Eastern Division.
New York (0-2-2) remained winless under new head Coach Mike Petke.
The Red Bulls' efforts to score an equalizer were hampered in the second half when Brandon Barklage was sent off for collecting his second yellow card after a foul on Bernier.
Celebrity Families of 2014 [PHOTOS]