Defender Mandela Egbo converted a penalty kick in the 14th minute and Ben Mines and Daniel Royer scored late in the second half for the Red Bulls (5-6-2, 17 points). New York improved to 2-0-1 in its past three road matches.
Former Red Bulls forward Juan Agudelo scored his 50th career MLS goal (49 regular season, one postseason) for Inter Miami (3-8-2, 11 points), who were unsuccessful in a bid for their first-ever two-match winning streak.
New York secured a 2-1 lead by taking advantage of Ben Sweat's turnover with a pretty passing sequence in the 49th minute. Florian Valot dropped the ball back to Omir Fernandez, who neatly set up White for the finish and his first career MLS goal.
Mines doubled the advantage in the 85th minute, cleaning up a rebound from Luis Robles (one save) for his first goal of the season and the second of his career.
Royer tallied six minutes later to cap the scoring.
The Red Bulls got the early jump after Inter Miami's Blaise Matuidi was whistled for a foul on Jared Stroud in the penalty area. Egbo made the expansion club pay by sending a right-footed shot into the bottom right corner of the net for his first career MLS goal.
Agudelo forged a 1-1 draw 25 minutes later as he chipped Matias Pellegrini's lead pass over the right arm of David Jensen (three saves). The goal was Agudelo's third of the season and second in as many matches.
The 27-year-old Agudelo began his MLS career with New York after signing a homegrown player contract in 2010. He recorded six goals and two assists in 33 matches with the club.