El Taib netted his first goal of the African campaign on 40 minutes to lift Benghazi from last to second in a match delayed 24 hours because Enyimba had flight and visa complications.
Orlando Pirates of South Africa top the table on nine points with one matchday to come, Benghazi have seven, Enyimba six and Entente Setif five. All four clubs have a chance of progressing.
The top two finishers qualify for the quarter-finals draw on April 30 in Cairo, where group winners and runners-up will be separated.
Benghazi visit Setif in the final round and a win will enable them to become the third Libyan club after Al Ittihad and Al Nasr to reach the knockout stages in the African equivalent of the UEFA Europa League.
As Enyimba sought an equaliser, they suffered a huge blow on 74 minutes when centreback Timothy Danladi was red-carded.
Benghazi had four players yellow carded and Enyimba three in a fiery clash that produced 47 fouls at the Martyrs of February Stadium in the eastern Libyan city.
The other three groups have been decided with JS Kabylie of Algeria, Coton Sport of Cameroon, Jaraaf of Senegal, CS Sfaxien of Tunisia, Raja Casablanca of Morocco and Pyramids of Egypt qualifying.