Tevragh defeated AS Real 1-0 in the Malian capital Bamako thanks to a 62nd-minute goal from Ely Cheikh Ould Voulani to book a date with Algerian powerhouses JS Kabylie.
The Mauritanians had been written off everywhere except at home after a goalless first leg and the dismal record of the country in the second-tier African club competition.
Clubs from the nation ranked 46 of 52 in Africa had lost five matches and drawn one during three previous appearances in the African equivalent of the Europa League.
Further Tevragh progress is unlikely, though, as Kabylie rank among the most successful teams on the continent, having won the African Champions League twice, the African Cup Winners' Cup once and the CAF Cup three times.
Kabylie had a first-round bye with 11 other contenders for the 660,000-dollar first prize, including FUS Rabat of Morocco, who stunned CS Sfaxien of Tunisia in the final last December.
Once-formidable Africa Sports of Ivory Coast and Daring Club Motema Pembe of the Democratic Republic of Congo also advanced to the last-32 stage, but failed to match good away performances.
Africa Sports could only draw 1-1 against Sequence of Guinea in Abidjan, with the 75th-minute lead Goue Blagnon gave the local club cancelled soon after by Aboubacar Camara.
Having returned from Conakry last month with a 1-0 advantage, much more was expected of the Ivorians, who reached four African Cup Winners' Cup finals between 1980 and 1999 and twice lifted the trophy.
Motema Pembe did win, 2-0 against Zanzibari visitors KMKM in Kinshasa via goals in each half from Nkanu Mbiyavanga and Bokota Labama, but expectations were high after a 4-0 first-leg triumph on the Indian Ocean island.
Burkina Faso armed forces club USFA are next up for Africa Sports, while 1994 African Cup Winners' Cup title holders Motema Pembe appear to have an easier task after being paired with Victors of Uganda.
Mohamed Aminu scored on 35 minutes in Obuasi as Ashanti Gold of Ghana overcame Sewe San Pedro of Ivory Coast 1-0 for the second time and Sahel of Niger and Missile of Gabon also progressed.