The Ferrari driver posted an ominously quick lap of one minute 47.299 seconds at the Marina Bay circuit on Saturday - over 1.7secs faster than his best time one day earlier.
Red Bull's Daniel Ricciardo came in just 0.051secs behind Alonso, with drivers' championship leader Nico Rosberg - who was hindered by the red flag following Pastor Maldonado's crash in FP2 - in third.
Rosberg's Mercedes team-mate Lewis Hamilton - who sits 22 points behind the German in the standings - endured a frustrating session, as he ran wide after locking up on Turn 13 of his fastest lap.
That meant the Briton, who went quickest in FP2, was sixth fastest on Saturday, some 0.439secs slower than Alonso.
Jean-Eric Vergne of Toro Rosso was also in impressive form as he pipped Red Bull's reigning world champion Sebastian Vettel - who has won the Singapore Grand Prix in each of the last three seasons - to fourth, while Williams duo Felipe Massa and Valtteri Bottas came in seventh and eighth respectively.
Alonso's Ferrari team-mate Kimi Raikkonen and Sauber's Esteban Gutierrez rounded off the top 10.
Qualifying for Sunday's grand prix takes place later on Saturday.