Messi and Suarez on hand to fire Miami into CONCACAF quarters
Messi set up Suarez for the eighth-minute opener and then the Argentine found the target himself in the 23rd minute.
But the eight-times Ballon d'Or winner was substituted in the 50th minute before his replacement Robert Taylor made sure of the victory with a 63rd-minute header.
Inter Miami coach Gerardo 'Tata' Martino said Messi's withdrawal, when he did not appear to limp or be in discomfort, was due to a concern about his hamstring.
"He has an overload in his right hamstring. So we didn't want to take any risks. We tried to see if he could hold on a bit longer but it was bothering him and we preferred to take him out of the game," he said.
"I imagine that for Saturday's game (at D.C. United) he is not going to be available," said Martino.
Miami, playing in the competition for the first time, will face the winner of Thursday's second leg between Mexico's Monterrey and MLS's FC Cincinnati in the quarter-finals.
The Liga MX team are at home and lead 1-0 from the first-leg.
The first-leg in Tennessee had seen Nashville take a two-goal lead before goals from Messi and Suarez inspired a comeback for a 2-2 draw.
And it was the former Barcelona pair that proved to be the difference again as Miami took control from the outset.
Messi had an early opportunity when he was brought down on the edge of the box, providing him with a free-kick from a central position but his shot struck the wall.
But minutes later, Messi created the opener, splitting the Nashville defence with a perfect pass to Suarez whose exquisite finish, with the outside of his right foot, matched the precision of the assist.
Messi on target
While the veteran quartet of Barcelona players in the Miami team, also including Spaniards Jordi Alba and Sergio Busquets, grab the attention, the young midfield workhouse Diego Gomez has become increasingly influential.
It was the Paraguayan's aggressive running that created the second goal, in the 23rd minute, when Gomez drove aggressively into the box and then smartly slipped inside to Messi who buried the ball, first time, into the corner.
It was Messi's fifth goal in five games in all competitions this season. Suarez has scored four in six games.
Nashville had created little but they offered a wake-up call to Miami keeper Drake Callender when Daniel Lovitz blasted a left-foot volley against the post.
Miami coach Gerardo Martino brought Messi off for Taylor five minutes after the interval, with no visible sign of an injury for the Argentine.
The departure of the eight-time Ballon d'Or winner gave Nashville a lift and they began to attack with real intent and Callender had to pull off a fine save at point blank range to deny Lukas MacNaughton.
But any hint of a Nashville comeback was snuffed out when Suarez turned provider with a delightful chip into the box towards Taylor who angled home his header to make it 3-0.
Nashville's Hany Mukhtar had an effort disallowed for offside before English striker Sam Surridge added a late consolation.
"We got the goals that we needed at the start," said Taylor.
"Then we knew in the second half they would try their all to score and they did put on more pressure. Luckily we got the third and Drake made some amazing saves. It is a great feeling going through and performing like this, every game is like do or die (in the Cup) so it's a great feeling," said the Finnish international.
Earlier Costa Rica's Herediano secured passage to the last eight with a 1-1 draw at Surinam's Robinhood enough to give them a 3-1 aggregate win.
Wednesday's later game is an all-Mexican clash with Club America defending a 3-0 first leg advantage at home to Chivas Guadalajara.
