Substitute Servando Carrasco scored the only goal of the match in the 34th minute as Orlando made it three victories from as many games in the club's new stadium.
Carrasco was introduced in the 17th minute as a replacement for injured midfielder Antonio Nocerino and the American made an immediate impact against the struggling Red Bulls in the Eastern Conference clash.
Will Johnson whipped in a corner and Carrasco headed home from close range as Orlando moved up to second in the East after four matches.
The Red Bulls are without a win in four games and sit seventh in the East, only two points adrift of Orlando, albeit having played two more matches.
Sporting KC extended its unbeaten start to the season after downing the Rapids 3-1.
Goals from Seth Sinovic, Gerso Fernandes and Dom Dwyer preserved Sporting KC's undefeated start after five games.
Kevin Doyle scored an injury-time penalty for the Rapids, who are ninth in the Western Conference and five points behind fourth-place Sporting KC.