Mikel excelled and Stamford Bridge team-mate Victor Moses slotted two late penalties as the Super Eagles overcame gallant Ethiopia 2-0 on Tuesday in this north-western town to finish second behind shock Group C winners Burkina Faso.
Zambia became the first defending champions since Algeria in 1992 not to reach the knockout stage after a 0-0 draw with the Burkinabe in Nelspruit near the world famous Kruger National Park game reserve.
A superior goal difference - plus four to plus two - gave Burkina Faso top spot ahead of Nigeria after both countries finished with five points, Zambia collected three and Ethiopia just one in a first appearance after 31 years.
Nigeria, who have failed to make the knockout stage only twice in 17 appearances, now adjust their sights to star-stacked Côte d'Ivoire and Mikel believes his country can send the Elephants packing.
"Playing against Côte d'Ivoire is going to be both tough and exciting and some of our opponents are my friends, especially Didier Drogba," said the 25-year-old Chelsea star.
"People who write off Nigeria do so at their peril. This is a knockout match that we can definitely win. The media keep reminding us that Côte d'Ivoire are unbeatable - we shall see.
"Ethiopia was a do-or-die game for us and we did really well, especially in the second half. Having conceded late equalisers against Burkina Faso and Zambia, we told the defence to improve their concentration and they did."
After Moses converted his first spot kick on 79 minutes before a big, vibrant Royal Bafokeng Sports Palace crowd, goalkeeper and acting captain Victor Enyeama made a spectacular diving save to prevent Ethiopia equalising.
Keshi celebrates with Nigeria
Qualification was particularly joyful for coach and 1994 Nigeria Cup of Nations-winning centre-back and captain Stephen Keshi after failing to get past the first round as a coach with Togo in 2006 and Mali three years ago.
"This is a victory for Nigerians where ever they are in the world," he told a packed post-match media conference. "This is a time for all Nigerians to celebrate.
"Now we face title favourites Côte d'Ivoire in the quarter-finals and there will be no second chance for either side. I have a game plan but, with respect, that is for the players and not for you guys (journalists).
"I am so proud of my boys and this is one of the best teams to represent Nigeria. We were hungry for a win tonight (Tuesday) after late equalisers robbed us of four points in earlier games.
"If we can keep this team together for the next two years I believe they will be virtually unbeatable. No one is giving us a chance against Côte d'Ivoire, but let us see what happens."
Ethiopia, who made eight changes from the team trounced 4-0 by Burkina Faso, collapsed in the closing stages and Moses scored again from the penalty spot on 90 minutes after being fouled by goalkeeper Sasay Bancha, who was red carded.
Côte d'Ivoire hold a slight edge over Nigeria at Cup of Nations tournament clashes, winning two and losing one of five meetings that produced a meagre seven goals.