Hamilton was 0.038 seconds faster than his fellow Briton, with Ferrari's Fernando Alonso, the championship leader, a further 0.020secs adrift.
Only 0.257secs separated the top eight, which did not include the Red Bulls of Mark Webber and Sebastian Vettel.
Webber and Vettel were 11th and 13th, with Vettel admitting: "There is a lot to go through and learn from."
Italian Grand Prix: First practice highlights
The reigning champion added: "We are probably more competitive in race trim but for sure today wasn't as good in terms of true pace. We can see we weren't quick enough."
The second Ferrari of Felipe Massa was fourth, ahead of Nico Rosberg's Mercedes and Kimi Raikkonen's Lotus.
Scot Paul di Resta edged out Force India's Nico Hulkenberg by just 0.001secs to take seventh.
Sauber's Sergio Perez was ninth, ahead of Michael Schumacher. The German legend,
who was fastest in the morning session,
was 0.804secs behind Button, but was hampered by a failure of his DRS overtaking aid early in the session, which would have cost him more than a second a lap.
In the morning session, Schumacher was 0.301secs faster than Button, who won the Belgian Grand Prix last weekend. Rosberg was third, ahead of Alonso, champion in 2005 and 2006.
“We can see we weren't quick enough. There is a lot to go through and learn from”
Despite his pace, Alonso, seeking to win his team's home grand prix for the second time in three years, had a troubled day.
He suffered engine failure in the closing minutes of the first session, then suffered a failure in the front-left brake system on the left-front corner when doing his fast run on medium tyres in the afternoon.
When he rejoined the track, the Spaniard managed one fast lap, marginally improving his time, before trailing into the pits at the end of the next lap with a gearbox problem.
The gearbox will be changed, but Alonso, who did not get a chance to do the usual race-simulation runs on the softer 'medium' tyre, will not incur a penalty because it was a practice unit.
Alonso failed to score any points after bring taken out in a first-corner collision cause by Lotus driver Romain Grosjean.
Webber is third in the standings, 32 points behind Alonso, with Raikkonen fourth a point further adrift. Hamilton is fifth, 47 points behind Alonso and Button sixth, 63 adrift.
McLaren sounded very confident during Friday's practice sessions.
Last five Italian GP winners
Sebastian Vettel (Red Bull)
Fernando Alonso (Ferrari)
Rubens Barrichello (Brawn GP)
Sebastian Vettel (Toro Rosso)
Fernando Alonso (McLaren)
Race engineer Dave Robson told Button over the team radio that his pace and tyre degradation looked "good", adding other cars may be faster but almost certainly on less fuel and suffering higher tyre degradation.
Mercedes also look set for a much stronger weekend than in recent races.
The long corners of the
which hosted the last two races, exposed the weaknesses of the car's aerodynamics.
But there are no long corners at Monza, while the long straights mean their straight-line speed boosting device, which stalls the front wing as well as the rear when the DRS overtaking device is activated, gives them a significant advantage.
It means that, in practice and qualifying at least, the team can either have a straight-line speed advantage for the same cornering performance, or give themselves more cornering pace by increasing the downforce without suffering the penalty on the straights that would normally create.
Saturday, 8 September: Third practice 09:55 BST; BBC Sport website text commentary. Qualifying 13:00; BBC Sport website text commentary and BBC Radio 5 live. Qualifying highlights: 17:30-18:45; BBC One.
Italian Grand Prix 2012, day three
Sunday, 9 September: Race: 13:00 BST; BBC Sport website text commentary and BBC Radio 5 live. Highlights 17:30-19:00; BBC One. Race highlights repeat: 0030-0200; BBC Two.
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