The Teranga Lions, runners-up to Algeria at the last Cup of Nations in 2019, needed 97 minutes to beat Zimbabwe, and were held by Guinea and Malawi, who are 109 places lower in the world rankings.
Malawi believed they should have been awarded a penalty in the second half when Gomezgani Chirwa had his shirt pulled by Bouna Sarr, but the referee disagreed after looking at the VAR monitor.
As Senegal sought a late goal, they introduced midfielder Pape Gueye off the bench in place of ineffective Boulaye Dia.
Gueye, barred by Fifa last week over a disputed transfer from Watford to Marseille, took his case to the Court of Arbitration for Sport (CAS) and won.
Chelsea goalkeeper Mendy and Napoli defender Koulibaly missed the first two matches and Paris Saint-Germain midfielder Gueye the second due to Covid-19.