Miami, without Messi, falls 2-1 in first leg to Monterrey
Miami had taken the lead through defender Tomas Aviles in the 19th minute but the game changed when Inter midfielder David Ruiz was sent off in the 65th minute.
Maximiliano Meza equalized four minutes later and then Jorge Rodriguez grabbed the late winner with a superb curling shot into the far corner.
Monterrey, level atop Mexico's Liga MX, will be strong favorites to advance to the last four of the regional tournament when they host the return game next Wednesday.
Miami will be hoping to have Messi fit for the second leg after he was again forced to sit out due to his hamstring injury.
Messi has missed Miami's past three MLS matches with the right hamstring injury but practiced on Tuesday morning, prompting suggestions he might be healthy for the first time since helping Inter reach the quarter-final by beating Nashville on March 13.
Against arguably the strongest opponents the Florida club have played, Inter coach Gerardo 'Tata' Martino set his team up in a defense-minded 4-5-1 formation with veteran Uruguayan striker Luis Suarez as the lone forward.
It proved to be a prudent approach with Miami's five-man midfield able to frustrate Monterrey and then look to break on the counter.
But the breakthrough came from a corner, whipped in low by Julian Gressel and met with a first time shot from Aviles which whistled home.
The Mexican struggled to break down Miami until Ruiz lashed out with his arm at the head of Meza right in front of the referee, who wasted no time in producing a second yellow card and the inevitable red.
Monterrey made the most of the numerical advantage and it took just four minutes for them to draw level when Sergio Busquets deflected a corner towards his own goal, 'keeper Drake Callender parried out but Meza was on hand to fire home the loose ball.
It was backs against the wall from then for Miami as they tried to hang onto the draw, but as they tired mistakes began to creep in and in the penultimate minute of regulation, Diego Gomez failed to control on the edge of the box, Meza fed Rodriguez and he curled a brilliant shot into the top corner past the diving Callender.
Martino said the dismissal would prove to be a learning moment for the 20-year-old Ruiz, who was handed a starting role due to a several injuries.
"It was a difficult situation for him. He did very well while he was on the field and obviously it is going to be a learning experience for him with the dismissal. For young players these are moments that serve you well as you grow in your career," he said.
Martino, who said Messi remained "game to game" in terms of a return, lamented the absence of several of his squad for such a big game.
"Monterrey was at full strength and we had important absences. The truth is that I liked the way we competed. We did very well," he said.
"We're practically at the beginning of a season, we have been competing for a month and a half... and it was hard for us to hold on physically when we were down a player.
"I can't have a negative view of what happened tonight because we competed well and we had seven players out of the team who give a lot of quality. But to start a season with a competition like this, you need the full squad to compete."