The 4-1 defeat was the heaviest suffered by global star Lionel Messi since moving Stateside.
Minnesota basked in the afterglow on social media, including taking aim at Miami with an Instagram post referencing their pink kit and Chappell Roan's song Pink Pony Club.
"Pink Phony Club" read the caption on an image featuring a goal celebration and shot of the overall MLS standings with Minnesota in fifth, a point ahead of Miami.
Irritated co-owner Beckham hit back in the comment section, saying: "Show a little respect @mnufc be elegant in triumph."
The former Manchester United and England star also went onto comment on their next Instagram post, which was captioned "49 years and counting" with an image of a giant banner reading: "History over hype. Culture over cash."
Beckham responded saying "respect over everything" in a comment featuring a pink heart emoji.
There was also a banner in the crowd stating 'No biting allowed' in a reference to Miami's Luis Suarez's history of biting opponents.
Miami were founded in 2018 and began playing two years later, with the side winning the Leagues Cup in 2023 during Messi's first season in Florida.
Former England captain Beckham, who shot to fame with Manchester United before moving to Real Madrid and, later, Los Angeles Galaxy, was one of the driving forces behind Inter Miami's creation.
