Lionel Messi into another final after producing heroics for Miami yet again
Miami, who won the Leagues Cup on penalties against Nashville on Saturday, are now one win away from their second trophy since Messi joined the club last month.
The US Open Cup is American football's oldest and most important knockout competition, dating back more than a century to 1914 and is similar to England's FA Cup or Spain's Copa del Rey.
Miami will host the Houston Dynamo in the final on September 27 after the Texan side beat Real Salt Lake 3-1 after extra time.
A month ago Cincinnati, who are top of Major League Soccer's standings while Miami are bottom, would have been clear favourites. But the Florida team are now a very different side to the one which was winless in their 11 league games before the arrival of the Argentine.
In the intense heat, with temperatures over 100 degrees fahrenheit (38 Celsius) at kick-off, Miami's unbeaten run since the signing of Messi and Spanish pair Sergio Busquets and Jordi Alba looked to be coming to an end.
Inter trailed 2-0 with 22 minutes remaining before the Argentine delivered two perfect assists to striker Leonardo Campana to take the game into extra-time.
Messi's compatriot Luciano Acosta had put Cincinnati ahead in the 18th minute and American striker Brandon Vazquez doubled the home side's lead with a fine strike from the edge of the box in the 53rd minute.
In the 68th minute, Messi whipped in a free-kick from the left which was headed home by Campana to breathe some life into what had been a tired display from Gerardo Martino's side.
Cincinnati thought that they had made it 3-1 but Yuga Kubo's effort was ruled out for handball.
In the seventh minute of stoppage time Messi, from deep on the left, swung in a glorious ball to Campana at the back post and again the Ecuadoran forward found the net to force extra time.
Miami went ahead in the first period with Benjamin Cremaschi sliding an excellent pass into the path of Josef Martinez and the Venezuelan made no mistake with a precise finish.
But Cincinnati bounced back in the second period with Japanese winger Kubo firing a right-foot shot into the far corner past the diving Drake Callender.
The teams were at 4-4 in the shoot-out when Callender saved Nick Hagglund's penalty for Cincinnati and Cremaschi converted the next to book Miami's place in the final.
The 18-year-old Miami-born Cremaschi, whose parents are Argentine, was congratulated by Messi after his match-winning spot-kick.
"I'm living a huge dream," he told CBS Sports, "Sometimes I sit down and really think about the position that I'm in and it's incredible, I never believed I was going to be in the spot I am in now," he said.
There was a more sober view from Martino, whose team must now begin their 12-game attempt to climb from last in the Eastern Conference to the play-off positions.
Martino suggested he may be forced to rest some of his players, including Messi, after an intense eight-game spell.
"Both Leo and many other players are reaching an important physical limit and from today we will evaluate how we approach the next three matches," he said.
"The fatigue is overcome with all the enthusiasm ... I hope the team in the future could play better, but it's very difficult to do that when you almost can't rest."
Houston took the lead on the stroke of half-time through Mexican international Hector Herrera but Salt Lake levelled with a Julio Anderson goal in the 64th.
Panamanian midfielder Adalberto Carrasquilla fired in a fine solo goal in extra-time before Luis Caicedo wrapped up the win at the death.