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).
Both teams had chances in a lively and fully committed encounter, leaving everything out on the field in Abidjan - but the match ultimately lacked real quality, especially in the final third.
Playing in their first-ever Nations Cup knockout game, Mauritania looked full of energy early on, with livewire runners bursting from deep, the lustrous gold trim and numbers of their kit sparkling in the late afternoon sunshine.
But it was Mendes who nearly broke the deadlock after nine minutes, racing on to a long ball over the top and lifting a delicate lob from distance over the despairing Niasse but wide.
It would have been a stunning opener.
After the fast start, the game turned scrappy midway through the first half and it was Lions of Chinguetti head coach Amir Abdou who began catching the eye more than the players on the pitch.
A nervous ball of energy dressed all in black, the man who also led Comoros to the last 16 in Cameroon two years ago never stopped marching back and forth in his technical area, gesticulating and barking instructions.
With most of the crowd backing Abdou's side, Mauritania dominated the early stages of the second period.
Aboubakary Koita put a direct free-kick on to the roof of the net before Souleymane Anne wasted his team's best chance just before the hour mark.
As Cape Verde's defence looked to block another surging run into the penalty area, the ball fell kindly to Anne, who blazed his left-footed effort high and wide when it looked easier to score, leaving the forward lying star-shaped on the floor in disbelief.
With extra-time beckoning, and with Mauritania beginning to tire, it was the Blue Sharks who pushed hardest for a winner.
Garry Rodrigues' powerful drive stung the palms of Niasse, parrying the ball as far as Jovane Cabral, who then saw his follow-up blocked.
From the resulting corner, Mendes' glancing header was also well saved.
But Cape Verde's all-time appearance holder was not to be denied, calmly converting the crucial penalty when it arrived to also extend his record as his country's leading goalscorer.
Ten minutes were added on but Mauritania never looked like finding an equaliser, meaning Cape Verde claim their first knockout win at an Afcon.