In difficult conditions at the Estádio Nacional 12 de Julho on an artificial surface, the Black Stars struggled to break down São Tomé and Príncipe.
Crystal Palace striker Ayew's 50th-minute penalty proved to be the decisive factor in their second Group C outing, moving Kwesi Appiah's side into top spot with six points.
Bafana Bafana's win over Sudan leaves them in second due to the head-to-head results, while Sudan and São Tomé are in third and fourth place - with three and zero points respectively.
Having only formed a football team through FIFA in 2005, Comoros, ranked 142nd, weren't expected to pull any surprises in Group G.
With seven-time champions, Egypt, Kenya and Togo group alongside them, the minnows followed up their impressive 1-0 win over Claude Le Roy's side with another historic result.
Hosting The Pharaohs in Moroni, Amir Abdou's side managed to hold them to a 0-0 stalemate, which will leave them at the top of the group after round two - irrespective of Kenya's result against Togo.