Messi scored two second-half goals, four minutes apart, after a first-half assist as Miami cruised to victory on Saturday (Sunday AEDT.
Neither team scored until German Berterame used assists from Messi and Luis Suarez in the final minute of the first half to score his ninth goal in his first 26 Major League Soccer (MLS) appearances.
Messi tied Los Angeles FC's Son Heung-min for the league lead with his 15th assist, becoming the first player in league history with at least 15 assists in three consecutive seasons.
Messi added his league-leading 24th and 25th goals in the 56th and 60th minutes for a 3-0 advantage.
The 39-year-old won the Golden Boot Award last season with a total of 29.
The Argentine icon and Josef Martinez are the only players in league history to score at least 25 times in a regular season twice.Â
Messi's 40 goal contributions are nine shy of Carlos Vela's record set in 2019 with Los Angeles FC, and the Miami legend has four matches remaining to break it.
Meanwhile, Rowles' D.C.United were thumped 4-1 in their away clash with Orlando City.
Rowles was part of the Socceroos' 2022 World Cup squad, starting in all four games as his side exited at the round-of-16 stage with a 2-1 loss to eventual champions Argentina.
But the defender failed to make the cut for this year's World Cup in the United States.
Antoine Griezmann had two goals and an assist as Orlando easily accounted for United, with his second goal coming after intercepting a misplaced pass by Rowles.
Elsewhere, Socceroos midfielder Aiden O'Neill copped a yellow card while playing a full 90 minutes in midfield for New York City FC in their 1-1 draw with Los Angeles FC.
With AP.
