Clad inskin tight body suits, they danced to the likes of Where Are U Now, Anaconda,Uptown Funk! and Hotline Bling at the Microsoft Theater in Los Angeles.
Recalling how she was inspired by past performances from the likes of musical icons Prince, Madonna and the late Whitney Houston and Michael Jackson, Lopez said: "This show truly inspired me and made me dream someday I would be one of the lucky ones who would perform on this stage for fans of music everywhere.
"That's why we all do this: to touch your hearts and give joy to you with our music. My dream has come true."
Based in Auckland, Royal Family made headlines recently for their work with pop superstars including Nicki Minaj, Justin Bieber and Lopez.
Kiwi dancers featured in a routine with J. Lo which opened the AMAs this year
J. Lo also made an impact with her impressive vocal introduction of 1999 hit Waiting for Tonight.
As the final note rang out and applause began, she urged people: "Wait, don't clap. Tonight's not about me. Tonight is about the music!
Goebel posted a message on Instagram thanking J. Lo for giving her the leg up which has seen her career soar to new heights.
"She gave me my first big break in the industry and to meet up three years later to put this together, so grateful for the opportunity to choreograph this," Goebel wrote.
It is the latest in a string of achievements for Goebel who recently choreographed a short film titled Purpose: The Movement, to coincide with the release of Bieber's new album.
Prince, who earned a rousing applause, presented the first award of the night to The Weeknd for favourite album - soul/R&B for Beauty Behind the Madness.
"Make some noise for Prince, ladies and gentlemen," said the singer, who performed later in the show.
