For the first time since the Canadian Grand Prix in June, a driver other than Nico Rosberg or Lewis Hamilton of Mercedes topped a Friday FP1 session.
Alonso, who was also fastest on that occasion, clocked an impressive time of one minute 49.056 seconds with approximately 30 minutes remaining in the session at the Marina Bay circuit.
Hamilton, whose victory at Monza at the previous race saw him close the gap to team-mate Rosberg in the drivers' standings to 22 points, was subsequently bumped down to second just 0.122secs adrift of Alonso.
Rosberg was just behind in third and the two Mercedes drivers will be confident of topping the timesheets as the weekend progresses.
Defending champion Sebastian Vettel posted the fourth-fastest time and looked strong in his Red Bull, but it was not all good news for the German as he suffered suspected engine failure at the end of the session.
Daniel Ricciardo has enjoyed an impressive debut campaign at Red Bull and he produced another solid display with the fifth-fastest time.
Jean-Eric Vergne of Toro Rosso was sixth, but he enjoyed a somewhat mixed FP1. A battery change meant he sat out the opening 30 minutes, before an energy recovery system failure brought an early end to his session.
Ferrari's Kimi Raikkonen was seventh ahead of McLaren's Jenson Button, while Daniil Kvyat (Toro Rosso) was ninth and Sergio Perez of Force India rounded off the top 10.