Equatorial Guinea, who stepped up to host the event at the last minute, were given little chance of getting through Group A, but took second spot after remaining undefeated.
Draws against Congo and Burkina Faso were followed by a decisive 2-0 win over Gabon on Sunday, with Javier Balboa and Iban Salvador scoring the goals.
Tunisia - ranked 22nd in the world and 2004 champions of the tournament - are also yet to taste defeat.
They topped Group B with one win and two draws, but Leekens is preparing his side for their toughest fight yet.
"We know we are not the best or the most beautiful, but we have qualified and I am very happy," Leekens is quoted as saying on FIFA's official website.
"We saw their [Equatorial Guinea's] match [against Gabon], the joy, we heard the car horns.
"They have a balanced team with a lot of pace up front.
"It won't be easy because they were fantastic. I am happy for the country, but now we want to qualify.
"It will be difficult because they will have the fans behind them, but I am quite confident. I try to be positive in any circumstance."
Only one side - Algeria - have scored more than Tunisia's four goals at the tournament.
Ahmed Akaichi has two of those and looms as a danger man for Leekens' side in this last-eight clash.
Equatorial Guinea are ranked 118th by FIFA and will be significant underdogs, though that does not concern Spanish-born midfielder Juvenal Edjogo-Owono.
"Our power now is that we are a united team," he said on FIFA's website: "
"In 2012, we had so many players who were not from our country and the fans were not happy about this and did not take as much pride as they now do about the national team."
Tunisia and Equatorial Guinea last played each other in qualifying for the 2014 World Cup, with the former prevailing 3-1 on home soil and the return match ending 1-1.
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