The Group C result in cold and windy northern Moroccan city Tangiers left the sides two points behind Libya, who outplayed Equatorial Guinea 3-0 in the first half of a double-header.
This is the third time Nigeria are trying to win the two-yearly championship for home-based footballers with their best showing so far being third place in South Africa four years ago.
Sunday Faleye, 37-year-old Rabiu Ali and Stephen Eze were foiled by the woodwork during a match which Nigeria dominated from start to finish.
Rwanda were content to defend and will look forward to meeting Equatorial Guinea next, knowing a win would put them in contention for a top-two finish and a quarter-final place.
Libyan Saleh Taher Saeid punished slack defending to score twice within 17 minutes of the kick-off and set up a convincing victory over debutants Equatorial Guinea.
A Zakaria Alharash tap-in three minutes from time completed a routine victory with all the goals created by Mohamed Aleyet.
On Tuesday, Group D kicks off in coastal city Agadir with Angola playing Burkina Faso followed by Cameroon against Congo Brazzaville.
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