Sainz fastest for Ferrari on his birthday at Monza
The Spaniard lapped Monza's 'Temple of Speed' with a best time of one minute 21.355 seconds with McLaren's Lando Norris second and 0.019 slower in a second session that was twice red-flagged.
Red Bull's Verstappen was top of the first session, in 1:22.657, ahead of a weekend that could secure him a record 10th win in a row.
Sainz was second fastest in that opening practice.
Verstappen was only fifth later on after a qualifying simulation run was slowed by traffic and he was turned down when he sought another go, with race engineer Gianpiero Lambiase determined to stick to the run plan.
"From my side, it probably could have been a little bit better, so still fine-tuning a bit the low-speed to the high-speed, but I’m quite confident of course that we’ll get there," said Verstappen.
"I think the running, in general, was okay, but in the short run I was blocked a bit in sector two, then in the long run, we didn’t really get to do a lot of laps."
Teammate Sergio Perez, second in the championship but now 138 points adrift after 13 of 22 races, was third fastest in both but halted the second session when he spun into the gravel at Parabolica with seven minutes remaining.
"I thought I had it under control but then I touched a little bit the gravel and that was it, game over," said Perez, who said the damage was slight and the Friday his best in a while.
Ferrari's Charles Leclerc and McLaren's Oscar Piastri were fourth in the first and second sessions respectively.
DOMINANT FORM
Verstappen won at Monza last year, with Leclerc starting on pole, and has been in dominant form this season with 11 wins so far.
He has equalled the nine in a row set in 2013 by now-retired Sebastian Vettel on his way to a fourth successive title with Red Bull.
Seven times world champion Lewis Hamilton, with a new contract keeping the Briton at Mercedes until the end of 2025, was eighth in the first session timesheets but only 17th in the second.
"It's been a messy day, partly with red flags but also because we've not got the car in a good place at the moment," said Mercedes' trackside engineering director Andrew Shovlin.
"That means we have a bit of work to do overnight to get the setup in the right place for the rest of the weekend."
Red Bull, Ferrari and Mercedes used only hard tyres during the opening session.
Both of the Ferrari drivers and Russell started the day with new power units, within their allocation of four for the season and therefore without penalty.
New Zealander Liam Lawson started his second grand prix weekend as a replacement for injured Australian Daniel Ricciardo at Italy-based AlphaTauri and was 13th and 18th fastest.
Brazilian reserve and F2 champion Felipe Drugovich replaced Lance Stroll at Aston Martin for the first session as part of a requirement to give young drivers track time and was 18th fastest.
Stroll then brought out the red flags at the Ascari chicane in the second session after his car suffered a fuel system problem and failed to set a timed lap.