The Briton, who trails team-mate Nico Rosberg by 29 points in the drivers' standings, was quickest in FP1 on Friday, but had to sit out the majority of the day's later session due to electronic problems as Rosberg went quickest.
However, it was Rosberg's turn to encounter difficulties in FP3 as his Mercedes hit trouble with the gearbox, meaning he was unable to post a completed lap before pulling out early.
That left Hamilton to lead the way for the German team, as the 2008 world champion posted the leading time just over halfway through practice before going even faster in the closing stages to clock a time of one minute 25.519 seconds.
Rosberg now heads into qualifying, which takes place later on Saturday, with work to do but the scene remains set for another fierce contest with Hamilton just a fortnight after the warring team-mates collided at the Belgian Grand Prix.
Ferrari are well backed by a partisan home crowd at the Monza circuit and the Italian fans witnessed Spaniard Fernando Alonso finish second quickest, some 0.412secs down on Hamilton.
Coming home third was Williams' Valtteri Bottas who continued his consistent weekend, while team-mate Felipe Massa was a close fourth.
Jenson Button faces uncertainty over his drive for McLaren next season but is enjoying a solid weekend in Italy and clocked the fifth quickest time, while defending world champion Sebastian Vettel (Red Bull) and Kimi Raikkonen (Ferrari) were sixth and seventh respectively.
Toro Rosso's Dani Kvyat was hit with a 10-place grid penalty earlier on Saturday after breaching FIA rules on engine changing, but the Russian responded with a fine session, finishing eighth.
Rounding off the top 10 were Red Bull's Daniel Ricciardo, winner of the last two races, and Force India's Nico Hulkenberg.