Leclerc lapped with a best time of 01:31.763 seconds, 0.076 quicker than Norris in an incident-free daytime session at the Marina Bay street circuit before the more meaningful night-time practice.
Leclerc and Norris, second in the championship but 59 points behind Red Bull's Max Verstappen, are the only drivers to have started on pole position in the last five races and qualifying will be crucial for Singapore where overtaking is difficult.
Triple world champion Verstappen was fourth fastest, 0.334 off the pace and complaining of understeer.
Ferrari's Carlos Sainz, winner in Singapore last season in Red Bull's sole defeat, was third and unhappy with his car's brake balance.
"We need to sort out the brakes," the Spaniard said over team radio. "It cannot be that we changed the brake balance so much."
RB's Yuki Tsunoda was fifth with McLaren's Oscar Piastri, winner in Azerbaijan last weekend, sixth after a close brush with the wall.
The Australian was delayed slightly after the rear-left wheel on his car jammed during pitstop practice.
Compatriot Daniel Ricciardo, whose future with Red Bull-owned RB is uncertain after the weekend, was seventh and ahead of Williams' Alex Albon, Aston Martin's Fernando Alonso and Alpine's Esteban Ocon.