Caden Clark and Cristian Cassares Jr. scored for New York (3-4-0, 9 points), which snapped a two-game losing streak.
-2021 MLS: All you need to know
The Red Bulls are a perfect 3-0-0 in their last three home games.
Silvester van der Water scored his first MLS goal for Orlando City SC (3-1-3, 12 points), who suffered their first defeat of the season.
The Lions had allowed only two goals in their first six games, but New York's signature high press tactics helped the Red Bulls control much of the action in the first half.
This pressure resulted in Clark's goal in the 35th minute. Patryk Klimala sent a pass across the box to Clark, who converted the chance.
It was the fourth goal of the season for Clark, who celebrated his 18th birthday last Thursday.
A foul on Clark just outside Orlando City's box set up the Red Bulls' next goal in the 60th minute. Cassares sent a well-placed free kick over the wall and into the upper-left corner for his third goal of the season.
van der Water gave Orlando some late hope with a goal in the 84th minute, however he missed a tremendous chance at the equalizer four minutes later. van der Water was wide open for a pass inside the Red Bulls' box but his shot missed the mark.
The Lions were playing without leading scorer Nani, who was serving the second contest of a two-game suspension for making contact with an official.
Joao Moutinho came off the Orlando bench to play 27 minutes. A hip injury has limited Moutinho to four games and only one start this season.
Klimala was making his first MLS start since signing a transfer deal with the Red Bulls on April 22.
New York midfielder Frankie Amaya was substituted out in the 43rd minute due to injury.
Caden Clark scores in Red Bulls' win vs. Orlando
Orlando City suffers its first defeat of the season at the hands of Caden Clark and the Red Bulls.