The reigning world championÃ¢â‚¬â„¢s time of 1:23.693 was a tenth of a second quicker than Red BullÃ¢â‚¬â„¢s Sebastian Vettel.
Friday morning practice presented a problem for a number of the leading teams over whether or not to run the McLaren pioneered F-duct, with the traditional low downforce set-ups that are unique to Monza believed to remove most of the advantage given by the F-duct.
Both McLaren drivers used the device in the first session, with Hamilton setting the third quickest time after Button and Vettel.
Robert Kubica continued to impress for Renault, carrying on where he left off in Spa two weeks ago to set the fourth-quickest time just ahead of MercedesÃ¢â‚¬â„¢ Nico Rosberg.
Then came a tight train of drivers headed by Mark Webber and followed by Vitantonio Liuzzi, Fernando Alonso, Felipe Massa and Michael Schumacher with Nico HÃƒÂ¼lkenburg close behind. Scot Paul Di Resta also impressed with a time of 1:24.923 as he replaced Adrian Sutil.
Virgin RacingÃ¢â‚¬â„¢s Timo Glock was quickest of the new teams with a 1:26.772, ahead of LotusÃ¢â‚¬â„¢ Jarno Trulli and team-mate Lucas Di Grassi, who were also sub 1:27.
The session was largely uneventful as all teams worked on their aero set-ups for the weekend, but Liuzzi, Schumacher and Hamilton all missed chicanes, while Hispania RacingÃ¢â‚¬â„¢s Bruno Senna, and WilliamsÃ¢â‚¬â„¢ Rubens Barrichello both failed to complete the session after suffering mechanical problems.
Monza is considered to be a strong circuit for McLaren, and with the power advantage from the Mercedes engine over Red BullÃ¢â‚¬â„¢s Renault power unit, there is pressure on championship leader Hamilton in what is seen as a Ã¢â‚¬Ëœmust winÃ¢â‚¬â„¢ race for him and the team who have recorded just two victories here in the last 12 years.
The Italian circuit is also special for Vettel, who two years ago secured his first pole position and race win in F1 for Toro Rosso, and the German must also win if he is to keep his world championship dream alive after a poor weekend at Spa. Meanwhile, FerrariÃ¢â‚¬â„¢s Alonso will be looking for his first win in Monza for the Italian team Ã¢â‚¬â€œ his only victory here coming during his ill-fated season with McLaren in 2007.
MORE: The latest football news
MORE: The latest tennis news