The 2012 winners have struggled so far in taking just one point from two games, and must improve in Ebebiyin to keep their dreams alive.
Even if they take all three points on Monday, Zambia will need Tunisia to avoid defeat against the Democratic Republic of Congo if they are to qualify.
Zambia have opened their scoring in each of their Group B fixtures to date, only for DR Congo and Tunisia to fight back.
A late Yassine Chikhaoui goal earned Tunisia all three points against Zambia on Thursday, but Honour Janza expects his side to bounce back with a win.
"We will not be banking on who wins [in the match between Tunisia and DR Congo], but our strength will be to win the last match," he said.
"So I think if we can win the last match then we can go to the table and check what will happened after that.
"We are still breathing, we are still in existence, so we will do our homework where the team made some lapses. We will improve on that so that we still maintain our status and we want to come out of the group as one of the best two."
Emmanuel Mayuka will not feature for Zambia, The Southampton striker has been ruled out of the tournament after suffering a groin injury following his goal against Tunisia.
A knee problem also robs Janza of midfielder Nathan Sinkala, placing more pressure on Rainford Kalaba and Evans Kangwa to shine.
Cape Verde know a point could be enough to earn a second quarter-final appearance in a row at the Cup of Nations, although they require victory to be certain of progressing.
Coach Rui Aguas has seen Cape Verde draw each of their matches to date, but is optimistic ahead of the clash with Zambia.
"I cannot criticise my players on the two games," he said. "We are confident that our third match will be different and that we will reach the quarter-finals.
"I think that we will ultimately score in our third match."
Zambia and Cape Verde went head-to-head during qualification for the tournament, with both recording home wins and the latter going on to top the group by a single point.
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