Mitrita led the way for New York after opening the scoring just 30 seconds into the match at Red Bull Arena on Sunday (AEST).
It was the fastest goal in New York's history and quickest in MLS since Allan Cruz's 28-second effort for Cincinnati in 2019.
After Cincinnati went close to equalising, Anton Tinnerholm doubled New York's lead from an acute angle in the 25th minute.
Mitrita made it a brace two minutes before half-time and Jesus Medina completed the scoring with two minutes remaining as New York moved up to fifth in the Eastern Conference, five points behind fourth-placed Toronto.
Elsewhere, Maynor Figueroa's 89th-minute equaliser rescued a 1-1 draw for Houston against Nashville.
Daniel Rios's 49th-minute goal had Nashville on track for maximum points until Figueroa scored from a set-piece.
Houston is ninth in the Western Conference, while Nashville sits ninth in the east.