The Eagles could not find the breakthrough despite being dominant in most part of the game, as the Rwandese team remained disciplined in the defence.
With the 3-0 convincing win over Benin Republic on Saturday, expectations were high for the Nigerians to come out with victory and maintain 100 per cent record in the qualifiers.
Only one change was made by coach Augustine Eguavoen from the last game, as Alex Iwobi made way for Fisayo Dele-Bashiru in the starting lineup, with Victor Osimhen starting from the bench like he did against Benin.
Nigeria took control of the game early on as expected with the rave of the moment Ademola Lookman tormenting the Amavubi defence. He thought he had given the Eagles the lead in the 22nd minute only for the effort to be ruled offside by the referee. A decision many Nigerian fans do not agree with.
The cancelled goal came after Victor Boniface had rattled the post, with the Eagles failing to convert the rebound.
Following the stalemate in the first half, Eguavoen made changes in the second, introducing Osimhen and Moses Simon who combined to give Nigeria a second goal against Benin.
However, the Amavubi who were inspired by the presence of President Paul Kagame remained resolute in the defence to ensure that no goal entered their net.
Even when Nigeria continued to pile the pressure towards the end of the game, nothing came out of it.
Despite the dropped two points, the Super Eagles remain top of the group with 4 points, followed by Rwanda with two points.
Nigeria will be hoping to return to winning ways when they host Libya in their next match in October.