The diminutive 24-year-old striker, on loan at second-tier Union SG in Belgium from English Premier League club Brighton & Hove Albion, scored with two powerful second half strikes to ensure the country finished second behind Nigeria in Group E.
Earlier on Sunday, Benin, the Democratic Republic of Congo, Tanzania and Zimbabwe also ensured qualification.
Benin beat neighbours Togo 2-1 in Group D to bring an end to the international career of former Arsenal, Manchester City and Tottenham Hotspur striker Emmanuel Adebayor.
Tanzania secured a convincing 3-0 home victory over neighbours Uganda, who had already qualified.
Tanzania finished second in Group L ahead of the small kingdom of Lesotho, who needed victory away in the Cape Verde Islands to qualify for the first time but were held 0-0.
Zimbabwe finished top of Group G with their 2-0 home win over Congo-Brazzaville, while DR Congo were second in the section after edging Liberia 1-0 in Kinshasa.
Khama Billiat and Knowledge Musona scored first-half goals for the Zimbabweans while Cedric Bakumbu was the Congolese hero.
South Africa, who had missed out on the last finals in Gabon two years ago, needed only a draw against Libya, who were forced to host the game on neutral territory in neighbouring Tunisia because of a FIFA ban on them hosting matches at home.
Libya would have qualified at South Africa's expense with a win and they dominated a goalless first half with Manchester-born Ahmed Benali at the centre of their attacks.
But Tau broke the deadlock after 50 minutes with a snap shot before Libya equalised with a Benali penalty in the 65th but the visitors restored their lead three minutes later when Tau fired in a shot from the left to ensure his country progressed.
The draw for the 24-team finals will be in Cairo on April 12. Cameroon won the trophy in 2017 by beating Egypt in Gabon.
The full list of qualifiers are: Egypt (hosts), Algeria, Angola, Benin, Burundi, Cameroon, DR Congo, Ghana, Guinea, Guinea Bissau, Ivory Coast, Kenya, Madagascar, Mali, Mauritania, Morocco, Namibia, Nigeria, Senegal, South Africa, Tanzania, Tunisia, Uganda and Zimbabwe
(Reporting by Mark Gleeson; Editing by Ken Ferris)
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