Hamilton, who is yet to win a race in 2022, saw off world champion Max Verstappen by 0.084 seconds with Ferrari's Charles Leclerc third.
Verstappen's Red Bull team-mate, Sergio Perez, took fourth, one spot ahead of Mercedes' George Russell.
Verstappen holds a 116-point championship lead heading into the concluding six rounds of the campaign.
He will win the title here on Sunday night if he takes the chequered flag, and sets the fastest lap, and Perez and Leclerc finish lower than fourth and eighth respectively.
The Dutch driver, celebrating his 25th birthday on Friday, led the way for the majority of the one-hour session at the Marina Bay Circuit.
But as darkness descended, Hamilton moved to the top of the timesheets to provide the British driver with early hope that he could force his way into contention.
Hamilton has won in Singapore on four occasions and set one of the laps of his life in qualifying for this race in 2018.
And the very early evidence suggests he might be able to take the challenge to Verstappen and his all-conquering Red Bull team.
The tight and twisty Marina Bay Circuit in the heat and humidity of Singapore is regarded as one of the most demanding challenges on the schedule.
Russell bumped the barriers at Turn 10 but limped back to his Mercedes garage without any damage.
The same could not be said for Lance Stroll after he made contact with the wall at the fifth corner and was forced to stop his wounded Aston Martin.
The session was suspended as Stroll's stricken car was removed from danger.
Alex Albon was back in his Williams three weeks after he suffered respiratory failure following complications from surgery. The London-born driver completed 20 laps and finished 16th of the 20 runners.
Lewis leads the way in FP1. Let’s keep this up, Team. ð pic.twitter.com/gg2aFu3IB1— Mercedes-AMG PETRONAS F1 Team (@MercedesAMGF1) September 30, 2022