Cesar Araujo scored twice and Mauricio Pereyra, Facundo Torres and Benji Michel all added goals for Orlando, while Lewis Morgan scored the lone goal for the visiting Red Bulls in the semifinal match between to the two MLS sides.
The first half was on track to finish scoreless until Morgan scored on a quick-hitting counter-attack for the Red Bulls and Orlando hit right back with Araujo knocking in the rebound from a corner kick that bounced off the far post to make it 1-1 at the break.
The hosts blew the match open at the start of the second half with a pair of goals as Mauricio Pereyra beat New York keeper Carlos Coronel in the 47th minute and Araujo added his second of the night soon after to give Orlando a 3-1 lead.
Torres put the match to bed before 80 minutes with a left-footed blast from 12 yards out and Michel capped it with a smooth finish to make it five on the night for Orlando, who will play the winner of Wednesday's other semifinal between the Sacramento Republic and Sporting Kansas City in the final.
The winner of the U.S. Open Cup receives $300,000 and a spot in next season's CONCACAF Champions League.