Nigeria had gone two goals up in the opening 17 minutes courtesy Odion Ighalo and Ahmed Musa, before Mohamed Zubya and Ahmad Benali levelled for the hosts.
However, Ighalo struck his fifth goal in three days against Libya, to seal three points.
“I congratulate my team for this victory. It was a huge test of our character.
“We lost a two-goal lead but fought hard instead of dropping our heads.
“We will stay humble because we have not qualified for Afcon yet. We keep fighting,” Rohr told NFF media after the game.
With this result, the three-time African champions top Group E with nine points after four matches.
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