Messi double keeps Inter Miami on top in MLS Eastern Conference
Miami suffered an early setback when their defender Franco Negri deflected a corner from Daniel Lovitz into his own net in just the second minute of the game at Chase Stadium.
Gerardo Martino's team have now failed to keep a clean sheet in each of their last 11 games and it could have been worse when three minutes later Josh Bauer blasted a shot against the bar.
But Messi soon had Miami on level terms - the Argentine set free by a clever flick from Diego Gomez saw a shot parried out by Nashville keeper Elliot Panicco, but after Luis Suarez directed the loose ball back to him Messi slotted home to make it 1-1 in the 11th minute.
Two minutes later, Messi took advantage of some sloppy play from Nashville but his low right-foot shot came out off the post.
Everything Miami was creating was coming through Messi, who flashed a snapshot wide before moments later whipping in a cross for a Gomez header which was saved by Panicco's feet.
Six minutes before the interval, Messi's former Barcelona team-mate Busquets found the net for the first time in MLS, meeting the World Cup winner's corner with a fine glancing header at the near post.
But there was a blow for the home side just before the break when Paraguay international Gomez was stretchered off with an ankle injury, the latest in a series of injuries for Miami.
His replacement, Brazilian born youngster Leonardo Afonso, had the ball in the net but his effort was ruled out for offside.
Nashville came out strongly after the break but despite dominating possession for the opening 20 minutes of the half, they had little to show for their efforts other than a couple of off-target long-range efforts from German Hany Mukhtar.
Nine minutes from the end, Miami were able to put the game to bed when Afonso was ruled to have been brought down inside the box by Bauer and Messi slotted home the penalty.
The goal was Messi's ninth goal in as many games in all competitions this season for Miami.
Martino was unhappy with the way his team had started so slowly.
"Regardless of how fortunate their goal was, we didn't start well in the first few minutes. They were more focused, more intense, they handled the ball better, they pressed," he said.
"There are a lot of things we need to correct, but I'd like to do it with the full squad. We have seven or eight players out which is a lot in a league as strict as MLS with the roster and budget issues," he said.
Miami have 18 points from their opening 10 games and Martino said that was a decent return considering the depleted squad he is working with.
"All this happens to us and we have still collected 18 points, which is significantly more than last year at this stage, we will be looking to accumulate points now so that the second part of the year is not as demanding and dramatic as last year," he said, referring to the ill-fated late chase for a playoff place.
Elsewhere in MLS on Saturday, champions Columbus Crew had to come from behind twice to earn a 2-2 draw with Phil Neville's Portland Timbers.
The leveller came in the 74th minute via a superbly struck long-range blast from French full-back Steven Moreira.
Last season's regular season table-toppers Cincinnati claimed an impressive 2-1 win at Atlanta United despite falling behind to a lovely, curling shot from Argentine midfielder Thiago Almada in the 59th minute.
The lead lasted just three minutes as reigning MLS Most Valuable Player Luciano Acosta led Cincy on a counter-attack and fed compatriot Luca Orellano to level.
Acosta completed a crazy five minutes when he grabbed the winner, tapping in after he was picked out by DeAndre Yedlin.
