Danladi opened the scoring in the 34th minute with a low finish set up by Angelo Rodriguez’s cross.
Rodriguez’s hold-up play led to a deflection that Romario smashed home with a volley in the 50th minute, giving Minnesota United (3-2-0) a 2-0 lead.
Cristian Casseres Jr. slotted in a putback to cut the Red Bulls’ deficit to one the 70th minute. It was the 19-year-old Venezuelan’s first MLS goal.
The Red Bulls’ Alex Muyl left the game in the 21st minute due to injury.
New York (1-3-1) lost its third in a row and lost back-to-back home games for the first time since May 2014.
Minnesota United ended its five-game road swing to open the season and will open its new stadium next Saturday, hosting New York City FC at Allianz Field.