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Chelsea captain Reece James opened the scoring with a 64th-minute free kick before the match was suspended for almost two hours due to lightning in the Charlotte area.
Angel Di Maria equalised from the penalty spot nine minutes after the restart but Benfica was reduced to 10 men early in extra time when Gianluca Prestianni was sent off for a second booking.
Chelsea then opened the floodgates as Christopher Nkunku, Pedro Neto and Kiernan Dewsbury-Hall netted in the space of nine minutes, setting up a clash with Brazil's Palmeiras next Friday.
The Premier League side dictated terms early at Bank of America Stadium as Enzo Fernandez and Moises Caicedo controlled the tempo in midfield.