Verstappen led the way in the opening running at the Marina Bay Street Circuit, but it was Hamilton's name at the summit by the conclusion of the night-time session.
Sebastian Vettel finished third for Ferrari, while Valtteri Bottas was fourth following his earlier crash.
Bottas' Mercedes mechanics performed a fine job to fix the Finn's damaged car to allow him to participate in the evening running.
Hamilton is bidding for a hat-trick of victories here on his unstoppable march towards a sixth world championship.
And the 34-year-old Briton appears in a good position to follow up his 2017 and 2018 triumphs with another win under the thousands of bulbs that light up the city-state venue.
Despite Hamilton's impressive Singapore record, the slow-speed track has been something of a bogey venue for his Mercedes team.
But the Silver Arrows look to be on top of the problems which have ensured they are not always the team to beat here.
On the evidence of practice, it could be a straight shootout between Hamilton and Verstappen after the Red Bull star finished 0.184 seconds off the pace.
Red Bull had been expected to run well this weekend, and in the hands of Verstappen, look poised to provide the greatest threat to Hamilton's chances.
Vettel was the only other driver within one second of Hamilton, but the German finished a full eighth tenths behind the Mercedes driver in his Ferrari.
Charles Leclerc arrived for the 15th instalment of the season as the sport's in-form driver following successive victories in Belgium and Italy.
But the Monegasque's weekend got off to an underwhelming start as a gearbox issue plagued his opening running before he finished only sixth later in the day.
Ferrari's powerful engine has less effect on the 23-corner street venue than the speedy Spa Francorchamps and Monza layouts, and Leclerc ended the day 1.2 secs down on Hamilton.
Alex Albon finished fifth for Red Bull, but a full second adrift of team-mate Verstappen.
The London-born Thai also broke his front wing after running straight on at Turn 10.
McLaren driver Lando Norris is racing in Singapore for the first time, and the British teenager finished an encouraging ninth, albeit two places and three tenths behind Carlos Sainz in the sister McLaren.
George Russell, also making his Singapore debut, was 18th for Williams.
Earlier, Hamilton's Mercedes team were fined £4,500 for a fuel breach during opening practice.