Norris lapped with a best time of one minute 30.727 seconds, 0.058 faster than Leclerc in a reversal of the first daylight session, and 0.629 clear of last year's winner for Ferrari Carlos Sainz.
Verstappen, 59 points ahead of closest rival Norris with seven rounds remaining, was 1.294 seconds off the pace with teammate Sergio Perez eighth at the winding Marina Bay street circuit.
Mercedes driver George Russell, who ended the night seventh fastest, crashed into the wall in the closing minutes at turn eight but managed to reverse out and return to the pits minus the car's front wing.
In a less serious incident, Argentine rookie Franco Colapinto pulled up at the Alpine pits instead of Williams and was waved onwards. He was 16th fastest with teammate Alex Albon ninth.
RB's Yuki Tsunoda was fourth fastest, ahead of McLaren's Oscar Piastri and RB's Daniel Ricciardo, whose future at the team is uncertain with Singapore possibly his last race, in sixth place.
Seven times world champion Lewis Hamilton, a four-time winner in Singapore, was 11th for Mercedes with Aston Martin's Fernando Alonso 12th.
Leclerc had set the fastest time of 1:31.763 in the incident-free first session, 0.076 quicker than Norris.
The pair are the only drivers to have started on pole position in the last five races and Saturday's qualifying will be crucial for Singapore, the only race Red Bull lost last season with overtaking always difficult.
