The son of a former footballer, Mbulu was based in Mozambique twice and Portugal before signing a three-year contract with South African Premiership club Baroka in 2019.
Hosts Malawi needed maximum points at Kamuzu Stadium in commercial capital Blantyre to secure a first appearance since 2010 while a draw would have sufficed for Uganda.
Victory temporarily took Malawi to the top of the table with 10 points — they were overtaken three hours later when fellow qualifiers Burkina Faso defeated South Sudan 1-0 in Ouagadougou.
Aston Villa forward Bertrand Traore scored the Burkinabe goal on 50 minutes as the team finished unbeaten a six-match qualifying campaign spanning 17 months.
Popularly known as the Flames, Malawi are ranked 123rd in the world, 40 places below Uganda, and will be making a third appearance at the finals after first-round exits from the 1984 and 2010 editions.
They are the 19th qualifiers after Algeria, Burkina Faso, Cameroon, Comoros, Egypt, Equatorial Guinea, Gabon, Gambia, Ghana, Guinea, Ivory Coast, Mali, Morocco, Nigeria, Senegal, Sudan, Tunisia and Zimbabwe.
