The Super Eagles failed to win or score in two previous matches, in Spain with a Catalonia side that included several Barcelona stars and in Portugal with fellow qualifiers Cape Verde Islands.
Russia-based Emmanuel Emenike – expected to spearhead the Nigerian attack at the Africa Cup with Ikechukwu Uche – scored the winner on 55 minutes in southern Portuguese resort Faro.
Efe Ambrose and Ahmed Musa combined to set up the striker and he scored from close range to compensate for the disappointment of having the ball in the net during the opening half only to be ruled offside.
Coach Stephen Keshi, who is going to a first Cup of Nations with his native Nigeria after taking Togo and Mali to previous African football showpieces, made a host of changes after his side took the lead.
Shock absentees from the last tournament a year ago, Nigeria qualified with comfortable aggregate victories over Rwanda and Liberia and have been placed in Group C with Burkina Faso, Ethiopia and defending champions Zambia.
Pundits have few doubts about the outcome of this mini-league with the Eagles and the Chipolopolo (Copper Bullets) strongly fancied to fill the top two places and advance to the knockout phase.
Meanwhile, Tunisia coach Sami Trabelsi has given his squad a verbal lashing after disappointing warm-up results with a narrow 2-1 victory over Iraq followed by 1-1 draws against Gabon and Ethiopia.
"My players did not perform well and all of them are in poor form," he told reporters in United Arab Emirates city Abu Dhabi, where the Carthage Eagles are preparing for the January 19-February 10 tournament.
"We are in trouble because the Cup of Natons is going to be much tougher and we are not ready for the difficult tasks that lie ahead. The squad has to do more and prove it deserves to wear the national colours."
Tunisia are hoping to organise an additional friendly against record seven-time African champions Egypt in the Middle East before facing Algeria, title favourites Ivory Coast and Togo in Group D – the group of death.
Egypt, who won an unprecedented three consecutive titles between 2006 and 2010, miss out on South Africa after suffering a stunning qualifying loss to Central African Republic.