A Philip Azango goal four minutes from time in Abuja earned them a 1-0 first-leg lead over 10-man CS Constantine of Algeria last weekend.
Nasarawa left it even later in the preliminary round to build a 2-1 advantage over Senegalese second division side Generation Foot, scoring the winner two minutes from time.
But they forced a 0-0 second-leg draw in Dakar to become the lone Nigerian survivors after Akwa United were surprisingly eliminated by V Club Mokanda of Congo Brazzaville.
United are in a slightly better position against Constantine, not having conceded a goal against the North Africans at the National Stadium in the Nigerian capital.
Coach Kabir Dogo believes the result in Senegal will heighten confidence among his players that they can survive again.
"We were written off after the first leg against Generation Foot only to silence our critics with a brave away performance," he told reporters.
"A lack of clinical finishing remains our major weakness and there will be great emphasis on that issue before the return match.
"Constantine are a good, typical North African club, but they are definitely beatable," added Dogo.
Constantine coach Didier Gomes Da Rosa blamed the Liberian referee for the loss after the early second-half red-carding of Hamza Boulemdais.
"Many of the decisions the referee made were incorrect and he caused our defeat," said the Franco-Portuguese handler.
Nasarawa are among five clubs playing away who are clinging to one-goal advantages in round-of-32 second legs in the African equivalent of the Europa League.
Al Ittihad of Libya, forced to stage home fixtures in Tunisia because of continuing post-Moamer Kadhafi-era lawlessness, take a 1-0 lead over Medeama to Ghana.
With domestic football impossible due to the security situation, playing in Africa is the only competitive outlet for Tripoli-based Ittihad.
Winners Hearts of Oak and Asante Kotoko contested an all-Ghana first Confederation Cup final in 2004, but the country has made minimal impact in the competition since.
Co-Confederation Cup leading scorer Arsenio 'Love' Cabungula will pose a threat for Sagrada Esperanca of Angola when they defend a 1-0 lead over Desportivo Maputo in Mozambique.
Stade Gabesien of Tunisia and Saint-Eloi Lupopo of the Democratic Republic of Congo are the other clubs travelling with one-goal advantages, but both conceded in 2-1 victories.
CAF debutants Gabesien face experienced Kaloum -- the first CAF fixture in Conakry since Guinea was declared Ebola free -- and Lupopo tackle Al Ahly of Sudan in Shendy.