Last year's race winner lapped the Hungaroring circuit with a best time of one minute 17.939 seconds, 0.117 quicker than Ferrari's Lewis Hamilton.
Formula One championship leader Kimi Antonelli was third fastest, 0.129 off the pace and ahead of Ferrari's Charles Leclerc, McLaren's Oscar Piastri and Mercedes teammate George Russell.
Red Bull's Max Verstappen was seventh on the timesheets, with teammate Isack Hadjar eighth but 1.004 off the pace.
Hamilton will be chasing his 10th Hungarian GP pole in later qualifying with the Briton also targeting a record ninth win at the circuit outside Budapest. Ferrari were fastest in both Friday sessions.
Antonelli, winner of six races so far this season, has a 45-point lead over Hamilton after 10 rounds.
The session was halted with 39 minutes to go when Cadillac's Sergio Perez stopped on track with smoking brakes and without setting a proper time.
Aston Martin's Fernando Alonso and Lance Stroll were 17th and 18th respectively with a heavily upgraded car, with the Spaniard 2.454 off the pace and the Canadian 2.994 slower than Norris.
Racing Bulls' rookie Arvid Lindblad managed only six laps after an engine change but was still 13th fastest.
Williams drivers Carlos Sainz and Alex Albon occupied the 20th and 21st positions respectively and were slower than Cadillac's Valtteri Bottas and the Aston Martins.