Nigeria could only manage a point in neutral Butare, Rwanda on Saturday after starting their bid to reach the global finals in the United States, Mexico and Canada with a desperately disappointing 1-1 draw at home to lowly Lesotho on Thursday.
The Super Eagles have therefore taken two points from their opening two games in the six-team Group C, with only the top side in each pool assured of one of Africa's nine automatic qualification places.
South Africa could open up an early four-point lead in Group C when they visit Rwanda on Tuesday.
Zimbabwe took the lead midway through the first half via Walter Musona, but Nigeria salvaged a draw when Kelechi Iheanacho equalised in the second half.
Zimbabwe are among the 19 African countries forced to move their home qualifiers to neutral venues because of poor facilities or security concerns.
Trezeguet scored a brace of goals as Egypt cruised to a 2-0 win over nine-man Sierra Leone in the Liberian capital of Monrovia, making it a full haul of six points for The Pharaohs in their opening two qualifiers.
The Leone Stars lost Tyrese Fornah to a first-half red card and never looked able to challenge Egypt after that as Mohamed Salah, who scored four goals against Djibouti on Thursday, completed another 90 minutes and provided the assist for his side's second.
The hosts also had Abdul Kabia sent off for a second bookable offence, while before that there were ugly scenes as several local fans invaded the pitch and at least one was involved in a fracas with Salah before being forcefully removed.
Algeria made it two wins from two but had to wait until the 69th minute to get the opener in a 2-0 victory in Mozambique. Fares Chaibi handed them the lead and Ramiz Zerrouki made sure of the points in the final 10 minutes.
Gabon have also made a perfect start to their Group F campaign after claiming a 2-1 victory against Burundi in neutral Dar-es-Salaam.
Jim Allevinah and Denis Bouanga scored in either half, before Abedi Bigirimana set up a tense finish when he pulled a goal back for Burundi near the end.
An own goal from midfielder Charles Pickel 11 minutes from fulltime gave Sudan a 1-0 win over the Democratic Republic of Congo in the Libyan city of Benghazi.
