The White Swans looked well on their way to the Final in the first leg as they got a two goal in the first period through Norihiro Kawakami, who scored a brace, but the Cheetahs showed the fighting spirit that have accompanied them this season by fighting back.
First Sobrie Mazelan pulled a goal just before the break and then in the second period Syaqir Sulaiman got the Cheetahs back on level term just 10 minutes before the end of the game to break the White Swans heart.
The second leg was no different as Albirex Niigata (S) took the lead in the game through Shotaro Ihata but Hougang United refused to die as the script demanded.
Basit Hamid, who came on as a sub, got the equaliser through an indirect freekick in the last 15 minutes after the Cheetahs had missed a penalty earlier in the game.
Neither side could get the winner in the remaining time thus extra-time was needed.
Yosuke Saito got the White Swans ahead again in that period but once again the Cheetahs came back as Sobrie Mazelan pulled the Cheetahs back on level term with 5 minutes to go.
That was when the Cheetahs make the mistake of the game as with a man advantage, with Albirex top scorer red-carded Shotaro Ihata, they went for the kill and left themselves short at the back.
The White Swans got their winner through a quick counterstrike as Hougang United lost the ball in midfield and with a 3on 3 situation, a pass found Yosuke Saito with space and time to take into the box and fired it into the top corner.
There was no coming back after this as Albirex reached their first ever RHB Singapore Cup Final.
Fadhil Salim (GK), Lau Meng Meng, Syaqir Sulaiman (Eddie Chang), Shariff Samat (C), Shahril Alias, Ratna Suffian (Sobrie Mazelan), Azhar Sairudin, Jordan Webb, Carlos Delgado, Noor Ali, Diego Oliviera (Basit Hamid)
Hougang UnitedRidzuan Hasan (GK), Lau Meng Meng, Syaqir Sulaiman (Raymond Kwa), Shahril Alias, Fathi Yunus, Ratna Suffian, Azhar Sairudin, Jordan Webb, Fazli Jaffar (Sobrie Mazelan), Noor Ali (C), Diego Oliviera (Basit Hamid)