A late Ryan Mendes penalty helped Cape Verde overcome Mauritania to book a place in the quarter-finals of the Africa Cup of Nations for just the second time.
The game looked set for extra-time until Cheick Elwely's careless defensive header inadvertently played in Benchimol, who was brought down by goalkeeper Babacar Niasse.
Captain Mendes did the rest, smashing his spot kick hard down the middle in the 88th minute.
The result sets up a quarter-final against either Morocco or South Africa on Saturday (20:00 GMT).