Villa scored the Manchester City-affiliate side's first ever competitive home goal in the 18th minute when he fired a low shot past Revolution keeper Bobby Shuttleworth.
The former Barcelona and Valencia star almost doubled his account shortly after when he got on the end of cross before firing wide.
Shuttleworth was equal to Villa's effort after the hour mark as the Spaniard searched for his second of the game.
The New York outfit almost made it 2-0 late on but Adam Nemec could only find the side-netting when he flashed an effort goalwards.
However, ex-Revolution man Mullins finally doubled the lead late on when he pounced on a square pass from Villa to slot home and claim the first win for the side.