Cameroon, Ghana, Morocco and Tunisia also booked their places in the finals on a frantic night of play-off action.
Senegal won the second leg of the African play-off 1-0 in Diamniadio thanks to a fourth-minute goal from Boulaye Dia and the teams finished level at 1-1 on aggregate after extra time.
As was the case in the Africa Cup of Nations final last month, Mane was entrusted with taking the crucial fifth Senegal kick and once again he made no mistake to give his side a 3-1 shoot-out victory.
Among the three Egyptians who failed to score in the shoot-out was Sane’s Liverpool teammate Mohamed Salah, who uncharacteristically blazed his kick over the crossbar.
Only four of the nine penalty takers were successful with captain Kalidou Koulibaly and Saliou Ciss missing for Senegal and Salah, ‘Zizo’ and Mostafa Mohamed for Egypt.
As Senegal celebrated a second straight qualification for the World Cup, Egypt were left to lament another dramatic loss to Senegal this year.