Messi had not made the trip to Atlanta, after a busy run of games since making his Miami debut in late July.
Miami coach Gerardo 'Tata' Martino said after the loss that he had been suffering from "muscle fatigue" and that it would have been "very reckless to bring him to play this game".
The 36-year-old sat out Argentina's World Cup qualifier against Bolivia in La Paz on Tuesday but watched his team-mates from the bench.
With no Messi last week, Miami defeated Sporting Kansas City 3-2 but this time it was a very different story for Martino's team.
Miami went ahead in the 25th minute with a superbly taken goal from in-form striker Ecuadorean striker Leonardo Campana.
But the response from Atlanta, sixth in the Eastern Conference, was emphatic with three goals in the space of eight minutes.
A glancing header from French midfielder Tristan Muyamba, which struck the inside of the post, was ruled to have crossed the line by the assistant referee.
Five minutes later, Atlanta had the lead when Brazilian winger Xande Silva dribbled to the byline and his pull-back was turned into his own net by Miami defender Kamal Miller.
Miami's defence, without former Spain international left-back Jordi Alba, were reeling and Brooks Lennon added the third in the 44th minute with a sweetly struck shot.
Miami got back in the game in the 54th minute through a Campana penalty but while they have made a habit of comebacks with Messi, there was no such revival this time.
As they pushed forward in search of an equalizer, Atlanta caught them on the counter with Greek striker Giorgos Giakoumakis slotting home his 14th goal of the season, bringing him level with Nashville's Hany Mukhtar as joint top scorer in MLS.
Another well-worked break resulted in the fifth in the 89th minute with Lobjanidze again the creator, setting up Tyler Wolff to blast home.
Miami remain next to bottom of the Eastern Conference, six points behind DC United who occupy ninth place, the last play-off spot.
Martino defended the decision to leave Messi and Alba - who he said also had muscle fatigue - at home ahead of a busy run of games with league matches on Wednesday and Sunday before the US Open Cup final on September 27th.
"We risked worse consequences if they came to play this game. It has nothing to do with the (artificial) surface," said the coach.
Comebacks
Eastern Conference leaders Cincinnati, already assured of a post-season berth, battled back for a 2-2 draw at last year's MLS Cup runners-up the Philadelphia Union.
A Jose Martinez goal and a penalty from Daniel Gazdag had put Philadelphia in command but the impressive Aaron Boupendza pulled a goal back for Cincinnati, in the fourth minute of the second half.
The visitors grabbed a point when Boupendza found Brandon Vazquez with a magnificent low ball and the USA striker found the net.
In-form Orlando City produced an even more impressive comeback at home to Columbus, winning 4-3 after trailing 3-1.
Ramiro Enrique levelled in the 86th minute with an opportunist strike and then won the game in the seventh minute of stoppage time, taking advantage of chaos in the Crew defence.
Earlier the 'Hudson River derby' between New York City and New York Red Bulls ended goalless.
Later on Saturday, Los Angeles FC host cross-city rivals LA Galaxy in their derby.
