The semi-final second leg at El Massira Stadium was overshadowed by chaotic scenes even before kick-off, as a pitch invasion delayed proceedings by 80 minutes.
USMA refused to leave their dressing room until they received assurances from Confederation of African Football (CAF) that conditions were safe, but once the match began, they showed impressive mental strength.
USMA struck first deep into first-half stoppage time when a VAR review resulted in a penalty for handball. Ahmed Khaldi kept his nerve to convert from the spot and hand the visitors a crucial lead.
The hosts responded in the second half, with Moussa Kone rising to head home the equaliser in the 75th minute. Despite the pressure, USMA held firm to progress on the away-goals rule after the first leg had ended goalless.
The encounter was heavily disrupted, with a total of 30 minutes added for stoppages - 20 of those coming in the second half due to repeated interruptions, including players going down injured and disputes over refereeing decisions.
"The credit goes to the players. It was a real battle, and we managed to get this qualification. It is deserved," said N'Diaye.
"The opponent came back to level the score, but we remained balanced. Even with the events surrounding the match, we managed to stay calm."
The Senegalese tactician also expressed frustration at the constant breaks in play, adding: "It's a shame to see so many stoppages in play, it breaks the rhythm and disrupts the players."