Bai struck the only goal on the hour mark to earn Kim Pan-Gon's hosts a deserved victory at the Mong Kok Stadium.
Hong Kong were only able to reach the second round of AFC qualifying, while Singapore were eventually eliminated in the third round.
However, Hong Kong produced a determined performance to survive an early assault from the visitors and claim the win.
Singapore started quickly and went close on a number of occasions in the early stages, strikers Qiu Li and Khairul Amri both seeing chances go begging in the first 20 minutes.
Hong Kong responded, though, midfielder Huang Yang forcing a fine save from Singapore keeper from Hassan Sunny from long range.
Godfred Karikari fired wide just before half-time, and shortly after the interval the hosts found the breakthrough their resilience had merited, Bai reacting quickest to find the net after Lee Chi Ho's header had been brilliantly saved by Hassan.
Singapore came close to levelling almost immediately, substitute Fazrul Nawaz touching Shakir Hamzah's cross just wide.
Still Hong Kong continued to threaten, and they were denied a second as Hassan denied Jaimes McKee after the striker had broken through the Singapore defence.
The visitors pushed to try and find an equaliser, but their efforts were to no avail as Hong Kong held on.
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