The Australian outpaced the Briton by three-tenths of a second ahead of both Ferraris as two crashes – involving Fernando Alonso of Aston Martin and Red Bull's Sergio Perez – brought out red flags.
George Russell of Mercedes was fifth ahead of Red Bull's struggling three-time world champion Max Verstappen, Alex Albon of Williams, Alpine's Esteban Ocon and Lance Stroll in the second Aston Martin. Nico Hulkenberg was 10th for Haas.
In a disrupted but dramatic session it was evident that Red Bull were unable to reproduce their normal dominating form, offering the prospect of a straight scrap between the McLaren and Ferrari teams in qualifying later Saturday.
Perez's late shunt at the Variante Alta led to a late scramble for drivers to set a fast lap time with Norris, upbeat after his maiden win in Miami two weeks ago, showing confidence to produce an improved time.
Verstappen was among those unable to find a quick qualifying-style lap in the final minutes of a confusing session with several drivers involved in entanglements that left many frustrated.
