The teams meet again next Tuesday in Mexico in the second leg of the home and home series to determine which club advances to the May 30 final.
Los Angeles FC and Mexico's Toluca begin the other semi-final tie on Wednesday.
After the start of the match was delayed by an hour due to a severe thunderstorm, Argentine right wing Correa scored the only goal just after the half-hour mark on a left-footed blast from outside the box into the lower left corner.
Nashville, which leads the MLS Eastern Conference, ousted Lionel Messi's Inter Miami in the round of 16 and beat Club America at Estadio Azteca in the quarter-finals.
Nashville began the MLS season 7-1-1 and leads Messi's squad by three points in the East.