The defending three-time world champion, who leads Rosberg by nine points in the title race, was second behind him in Friday's opening session.
On a hot late summer's afternoon at the old Autodromo Nazionale in Monza's former royal park, the 31-year-old Briton clocked a best lap in one minute and 22.801 seconds to outpace German Rosberg by 0.193 seconds.
Hamilton is seeking to complete a hat-trick of successive Italian wins and to claim his 50th Formula One victory in Sunday's race.
Under-scrutiny Dutch teenager Max Verstappen, who was given a gentle warning about his aggressive style of driving by the FIA's Race Director Charlie Whiting earlier in the day, was fifth ahead of his Red Bull team-mate Daniel Ricciardo.
Former Ferrari driver Fernando Alonso was seventh for McLaren ahead of Valtteri Bottas of Williams with Romain Grosjean of Haas and Jenson Button, in the second McLaren, completing the top ten.
Verstappen and the Red Bull team manager Jonathan Wheatley met Whiting before the morning practice to discuss Verstappen's performance at last Sunday's Belgian Grand Prix.
After the meeting Red Bull team chief Christian Horner told reporters that Whiting had told Verstappen he risked disqualification if continued with the aggressive style that prompted criticism from both Ferrari drivers and others.
He said: "Charlie was keen to show him a video of Spa. It was a gentle warning... Like any 18-year-old, the criticism (from other drivers) seems to be going in one ear and out the other. He really doesn't care."
Hamilton had managed a clean sweep last year by topping all the practice sessions and taking pole position en route to victory, but his hopes of a repeat were ended by Rosberg in the first session.
Rosberg is seeking his first victory at the Italian Grand Prix.
Brazilian Felipe Massa, who on Thursday announced his impending retirement from F1, was 11th in his Williams and Kevin Magnussen, who limped away from a high speed crash in his Renault in Belgium last Sunday, was 19th.
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