The draw means at least one more of the continent's top contenders will miss out on next year's tournament in South Africa, joining record winners Egypt on the sidelines.
The Ivorians host the first leg of the knockout clash in September and then travel to Dakar for the return in October.
For a golden generation of Ivorians players, who have been to two successive World Cups and reached the final of two of the last four Nations Cups, it presents a tough test.
It is also arguably the last chance for the likes of Didier Drogba, Kolo Toure and Didier Zokora to live up to their role as kingpins in Africa's top-ranked team and win an elusive continental championship.
The Ivorians did not concede a goal at the finals in Equatorial Guinea and Gabon earlier this year, but still contrived to lose the penalty shoot-out in the final against Zambia.
A highly fancied Senegal, boasting a number of European-based players, went to the 2012 finals as best performer in the preliminaries, only to lose all three group games and suffer the embarrassment of being the first team eliminated.
Despite that setback, they were expected to provide another credible challenge at the 2013 tournament, but to do so now will first need to get past the Ivorians.
Thursday's draw in Johannesburg also produced derbies between Sudan and Ethiopia, who both played at the first Nations Cup in 1957, and Algeria and Libya.
Egypt, who have won a record seven Nations Cup titles, were knocked out in the first qualifying round last month. Their conquerors, the Central African Republic, must now beat Burkina Faso to secure a first finals appearance.
The qualifying ties will be played on the weekends of September 7-9 and October 12-14.
The 15 winners join hosts South Africa in the finals from January 19-February 10 next year.