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.

Scot Muir, 23, has already broken the European 3,000m and British 5,000m indoor records this year, and also took Holmes' British 1,000m indoor record.
Holmes, who won Olympic gold in both the 800m and 1500m at Athens in 2004, has been impressed by her displays.
"Laura has already taken the world by storm," she told Scottish Athletics.
"She truly can go all the way in the sport - and by that I mean start to medal at major championships."
Muir will attempt to win her first major medals at this week's European Indoor Championships in Belgrade, where she will run in both the 1500m and 3,000m.
She will then switch her attention to her main target this year - the World Championships, which take place in London from 4-13 August.
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Speaking to BBC Scotland last month, Muir said she viewed a "home World Championships" as "big", especially having seen the impact of the 2012 Olympics in London.
Holmes said: "Laura first came to my attention when she was fifth at the World Championships in Beijing in 2015.
"She is an unassuming girl in some respects, but you can see she is a very strong runner."
Holmes added Muir had shown she can run fast but must now "translate that by racing well on the world stage".
She added: "Championships are all about placings and, at only 23, Laura has already taken the world by storm.
"I believe that, in 2017 at the World Championships, she can cement her place in history."
Holmes believes young Scots - particularly girls - can look to the likes of Muir, Eilidh Doyle, Lynsey Sharp and Eilish McColgan for inspiration.
"Role models are important in society generally, but role models from the world of sport I believe have the most credibility - especially if you are trying to inspire girls and women," she added.
"Scotland have had some amazing talent in the past and it looks like it is continuing."
Muir, the 2016 Scottish Athlete of the Year, will begin the final year of her five-year veterinary studies a week after the World Championships, continuing to combine them with her running career.
The British Lionhearts made a winning start to their latest World Series of Boxing campaign, with an away victory over USA Knockouts.
[NEXT_CONCEPT]
Laura Muir can "cement her place in history" by winning a medal at the World Championships this summer, says ex-Olympic champion Dame Kelly Holmes.