Atlanta made its debut on Monday (AEDT) after Minnesota United's bow on Saturday as the league expands from 20 to 22 teams this season.
But the Red Bulls spoiled the party thanks to late goals in front of 55,297 fans at Bobby Dodd Stadium in Atlanta.
Led by former Argentina and Barcelona head coach Gerardo Martino, Atlanta dominated proceedings and threatened to overrun the Red Bulls, with its pace and penetration resulting in the 25th-minute opener.
A cross from Tyrone Mears found its way to Yamil Asad at the back post and the Argentine midfielder - on loan from Velez Sarsfield - made no mistake from inside the six-yard box to celebrate Atlanta's first MLS goal.
Atlanta's lead should have been more and the Red Bulls capitalised in the second half thanks to Daniel Royer in the 76th minute before Tottenham loanee Anton Walkes turned the ball into his own net six minutes later as the visitors from New York silenced the host.
It was also a landmark night as Orlando opened its new stadium with a 1-0 win over New York City.
Cyle Larin ensured Orlando's stadium opener resulted in maximum points, despite an injury to captain Kaka in the first half.
Kaka was forced from the field with a hamstring strain in the 11th minute but Larin's close-range header four minutes later downed David Villa and Andrea Pirlo in front of a capacity crowd.
Meanwhile, Vancouver Whitecaps and Philadelphia Union played out a goalless draw.