Atlanta United triumphed 3-2 in the best-of-three decider in Fort Lauderdale, Florida, after both sides had won one game each.
Miama finished the regular season with a record 74 points from 34 games in the Eastern Conference to win the Supporters’ Shield.
Miami took the lead at Chase Stadium when Matias Rojas scored from a rebound after former Aston Villa keeper Brad Guzan had denied Argentina forward Messi.
Two goals in two minutes from Jamal Thiare put Atlanta in front and, despite Messi equalising with a header, Bartosz Slisz scored the winner as Miami appealed for play to be stopped with defender Tomas Aviles lying on the pitch injured.
Last month Miami, who are co-owned by David Beckham, were named as one of the 32 sides in next year’s expanded Fifa Club World Cup.
“They are now officially one of the 32 best clubs in the world, already after a few years since their existence,” said Fifa president Gianni Infantino.
“And now they can start writing their story also on the global stage.”
In December Miami signed Uruguay striker Luiz Suarez, reuniting him with former Barcelona team-mates Messi, Sergio Busquets and Jordi Alba.
Atlanta scraped into the play-offs by finishing ninth in the Eastern Conference, then beat Montreal on penalties in a wildcard game to set up a meeting with Miami.
Atlanta will play Orlando City, and New York City face New York Red Bulls, in the semi-finals,, external which are decided by one game rather than three.
The winners will meet in the Eastern Conference final, and the winners of that will play the Western Conference play-off champions in the MLS Cup final on 7 December.
“This season has had good and bad things,” said Miami manager Gerardo Martino.
“If you think about the expectations we had for this play-offs, obviously we came up a little short.
“The players are sad, as they should be when there are so many expectations and the team can’t fulfil them.
“In this final part of the year we got used to achieving the objectives but we couldn’t achieve the most important one.”
Miami defender Alba said the MLS Cup format is “a bit unfair”.
“It’s been done for many years but I think it should be the champion of one conference against the champion of the other to make it as fair as possible,” he said.