The Brit, looking to regain some momentum in his title battle after retiring in Zandvoort last week, topped the timesheets with a 1:19.878s, just under a tenth ahead of the Monegasque.
Leclerc did not have a faultless hour, however, skidding off onto the gravel run off at the Ascari chicane with just a few minutes left to go.
Carlos Sainz was third, matching his FP1 result, with Norris' team-mate and title-leader Oscar Piastri fourth.
Lewis Hamilton, who topped FP1 to the delight of the watching tifosi, was fifth, with Max Verstappen sixth, the top six covered by just two tenths.
Alex Albon was seventh, with Nico Hulkenberg eighth, and Yuki Tsunoda ninth, two tenths off Verstappen's time in the sister Red Bull.
George Russell, whose Mercedes stopped out on track earlier in the day, was 10th, with Isack Hadjar 11th.
Gabriel Bortoleto and Lance Stroll were next, with Oliver Bearman and Fernando Alonso 14th and 15th.
Esteban Ocon was 16th, followed by Liam Lawson and Pierre Gasly.
The session was red flagged just before one-third's distance after Andrea Kimi Antonelli spun and beached his Mercedes on the exit of the second Lesmo.
It was the last thing the Italian rookie needed, amid increasing talk of his performances and at what is his first fully home Grand Prix as an F1 driver.
This left the rookie 19th, with the Alpine of Franco Colapinto propping up the order in 20th place.