Faleye went close again on 20 minutes after he was played through on goal by Rabiu Ali but Rwandan keeper Eric Ndayishimiye quickly came off his line to stop his effort from going in.
The Eagles continued to create the better opportunities and were almost rewarded in the 21st minute but Anthony Okpotu saw his header go just over the bar after the Rwandan keeper’s failure to claim a long throw.
In the 26th minute, Rwanda had their first attempt on goal but goalkeeper Ikechukwu Ezenwa was in the right position to stop a goal bound shot.
On 34 minutes, the Eagles were awarded a free-kick on the edge of the box after a foul on Faleye but Osas Okoro’s effort was blocked by the Rwandan defensive wall.
Stephen Eze went close on 37 minutes after connecting with a header from Daniel Itodo’s long throw.
A minute later, Ali should have scored from close range after Rwanda keeper poorly punched Okoro’s cross but the Kano Pillars midfielder hit his left-foot strike just over the bar.
Ali went close again in the 42nd minute but saw his long range shot hit the cross bar.
In the 51st minute, Rwanda went close following a dangerous ball across the Eagles box which went away from danger.
Eze thought he had opened the scoring in the 58th minute for the Eagles but his effort was ruled out for offside.
Rwanda ventured forward in the 62nd minute but Kalu Orji made a timely clearance to avert the danger.
With 12 minutes left, substitute Mustapha Ibrahim saw his header from a corner hit the post before the rebound was cleared by the Rwandan defenders.
In the 87th minute, Ali attempted a left-foot strike in front of the Rwandan box which went wide.
The Eagles’ next game is on Friday, 19 January against Group C leaders Libya who thrashed Equatorial Guinea 3-0 in the first game of the group.