Harvey Horn, Pat McCormack and Lawrence Okolie each secured wins to complete a 3-2 scoreline in Miami.
In an exciting finish to the contest, heavyweight Okolie's fight went to a split decision in the deciding bout.
World Series Boxing offers fighters a route to Rio 2016 via an Olympic qualifying event in Bulgaria in May.
Team GB topped the boxing medal table at London 2012, with three gold medals, one silver and one bronze.
The Lionhearts' next match is away to the Morocco Atlas Lions on 5 February in Casablanca. The team's first home fixture will be against the Mexico Guerreros at York Hall on 18 February.
The British Lionhearts made a winning start to their latest World Series of Boxing campaign, with an away victory over USA Knockouts.