The Briton lapped the Hungaroring with a best time of one minute 16.098 seconds on new soft tyres with Australian Piastri a mere 0.044 slower.
Red Bull's triple world champion Max Verstappen was third fastest, 0.281 off the pace, with George Russell fourth for Mercedes on a cooler afternoon than Friday's scorching temperatures.
Verstappen leads Norris by 84 points in the Formula One championship after 12 of 24 races and is going for his third successive Hungarian victory.
Ferrari's Carlos Sainz was fifth fastest while team mate Charles Leclerc, who crashed on Friday, was only 11th.
Australian Daniel Ricciardo was the sixth quickest for RB, ahead of Williams's Alex Albon, Haas's Nico Hulkenberg, RB's Yuki Tsunoda and Mercedes's seven-times world champion Lewis Hamilton completing the top 10.
Qualifying was following later at the Hungaroring.
