Gabon have only made the last eight on two previous occasions, including in 2012 when co-hosts Equatorial Guinea also made their only appearance to date.
This year's hosts are yet to win a match, having been held by both Congo and Burkina Faso, while Gabon have one win and a defeat to their name.
Sunday's Group A fixture will be the first AFCON meeting between the sides, and Equatorial Guinea coach Esteban Becker believes his side can continue to make a mark at their home tournament.
Speaking after Wednesday's goalless draw with Burkina Faso, Becker said: "The Burkinabe had so many players from top-flight European leagues.
"We were like ants compared to them - amazing ants.
"I am so proud of this squad, who want to defend the honour of the nation.
"They are mainly young and all are hungry for success."
Gabon have lost just one of their last 10 matches against Equatorial Guinea, so will be confident of making a rare foray into the knockout stages.
However, that defeat came in 2003 in the last competitive meeting between the sides, meaning Gabon will have to be on their guard this time around.
While a draw would be enough for Gabon, who will be keen to see Pierre Emerick-Aubameyang back among the goals after missing a golden opportunity on Wednesday, hosts Equatorial Guinea need a win.
Gabon head coach Jorge Costa said: "My players are feeling good physically, they are feeling good mentally. They know what we need to do.
"The atmosphere is great and we are going there with confidence. I am sure tomorrow's game will be a beautiful show for the last game of the group stage. We will give everything and play to bring back the three points.
"The only thing that matters is to get those three points. I don't make any plans further. The only good thing is we have our destiny in our hands."
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