Max Verstappen - who can score a record-breaking 10th grand prix victory in succession this weekend - was only fifth fastest but found traffic on his soft tyre run, while team-mate Sergio Perez was third but ended his session in the gravel at Parabolica.
In a bid to avoid the chaotic scenes of recent years at Monza, the FIA has implemented a minimum lap time designed to stop drivers from crawling at low speed in order to create space for a hot lap.
FP3 will get under way at 11:30 BST with qualifying following at 15:00 BST.
Piastri gets it too hot into the second chicane, Variante della Roggia, and has to skip over the gravel on the exit. McLaren ask him to pit to check for damage.
Alonso is being held up by traffic and says "they will have a bad surprise in qualifying" referring to the tighter rules on minimum lap times. Meanwhile, Norris has to put two wheels on the gravel to avoid a wandering Alfa Romeo.
Hulkenberg takes inspiration from the locals with a very Italian hand gesture aimed at an Aston Martin mechanic standing in his way as he dived into the Haas pit area.
While Sainz has kept Ferrari at the sharp end this weekend, it has been a more sedate affair for Leclerc so far. He is eighth and three-tenths off his team-mate - but a second off Verstappen.
Piastri makes his first outing of the day just over 15 minutes into the session. He's straight into a soft tyre run and his first timed lap puts him in 11th.
Tsunoda has to squeeze past one of the Ferrari cars that was touring in the middle of the track around Curva Grande. To the surprise of nobody, that is followed by pure fury from the Japanese driver over team radio.
Norris, also on softs, pushes Perez off his perch with a 1m22.515s. Sainz, waving to the tifosi throughout his out-lap, is straight into a soft tyre run as he looks to repeat his Friday efforts.
With this weekend also running the Alternative Tyre Allocation, there's an even more pick-n-mix of compounds between the drivers right now. Perez, on softs, leads the early times with a 1m22.662s.
That trio is joined by nine others, including Hamilton, who wasn't happy with his wing levels and set-up in FP2 which couldn't be fully changed in time before the end of the session. So his improvements will be one to keep an eye on.
Off we go for FP3. Bottas, Stroll and Hulkenberg are the first early takers. No surprise to see Stroll out early given he was sidelined for FP1 with Drugovich in the car and then he completed just two laps in FP2 before a fuel systems issue which forced him to park up.
One big talking point for today will be traffic. Not the kind trying to get in and out of Monza, but the congestion on the track. The FIA has moved to avoid any further chaos by expanding its use of minimum lap times to stop the dawdlers. Full story here.
The drivers are in the garages ahead of the session, which will be run in bright and warm sunshine, with the temperatures already hitting a pleasant 26.1C.
Yesterday it was Carlos Sainz's birthday, today it is McLaren's birthday! It is 60 years to the day since the racing team was founded. Beats! Beats! Beats!
After some Ferrari cheer on Friday, can it be followed up today? Sainz, who topped FP2, is quietly confident it can put up a fight against the dominant Red Bull and Verstappen combination.
