It 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 two Nations Cups in the last six years, it presents a tough test in arguably the last chance for the likes of Didier Drogba, Kolo Toure and Didier Zokora to live up to their billing as Africa's top ranked team and win a continental championship.
The Ivorians did not concede a goal at the Afcon in Equatorial Guinea and Gabon earlier this year but still contrived to lose on post-match penalties in the Final against Zambia.
Senegal went to the 2012 tournament as the best performer in the preliminaries and were highly fancied, but despite a squad filled with European-based professionals they lost all three group games and suffered the embarrassment of being the first team eliminated.
Despite the setback, they were expected to provide another credible challenge in 2013 tournament but in order to do so must now 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 get past Burkina Faso in order to secure a maiden 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 Jan 19-Feb 10 next year.