Liberia took the lead in their Group C tie just before the breakthrough Van-Dave Harmon’s well-taken striker given his side a first-half lead.
In the second half, the white-shirted Blue Sharks rallied from behind to score twice from two substitutes, including an injury-time screamer from Garry Rodrigues.
Jamiro Meitero had levelled the scoreline in the 52nd minute before Garry Rodrigues last-gasp winner to stunned the West Africans.
As a result, Liberia is sitting bottom of the group with three points from their last three games.
Elsewhere, Super Eagles were stunned after substitute Karl Namnganda scored a dramatic 90th-minute goal as Central African Republic registered their first group win as they bid to reach Qatar 2022 FIFA World Cup.
Namnganda came off the bench in Lagos to make only his second appearance for his country after being substituted when he debuted against Liberia last month.
He silenced Nigerian supporters by winning a sprint down the middle of the pitch against two defenders and firing a low shot past goalkeeper Francis Uzoho.
Nigeria, however, still leading the group after winning their first two matches.
Cape Verde host Liberia on Sunday while Nigeria takes on the Central African Republic in the group next matches.
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