Amid speculation about his future and a possible switch to Mercedes, Hamilton took his fourth pole of the season in a time of 1 minute, 24.010 seconds, just over a tenth of a second faster than Button.
Ferrari driver Felipe Massa was third — much to the delight of the home fans — but championship leader Fernando Alonso had another disappointing day. The Spaniard, who was just a thousandth of a second behind Hamilton in the final practice, will start way back in 10th position in Sunday's race.
Hamilton has been in good form all weekend, topping two of the three practice sessions, a week after getting into trouble with his team after posting sensitive data on Twitter. He has yet to commit to staying with McLaren, which has fueled talk about a possible move to Mercedes.
"I haven't had any distractions this weekend, so it's been quite positive...pretty smooth so far," Hamilton said. "It's been a tough weekend but we've managed to work on the setup and the guys done a fantastic job. So, congratulations to the team. It's great obviously for the team to have me and Jenson at the front."
Hamilton, however, wasn't completely satisfied with his performance in qualifying.
"I think practice was a lot better for me," he said. "I had much, much better laps in practice but I can't complain. Generally I didn't think that lap was anywhere near good enough.
"But nonetheless I'm happy and I'm really happy for the team because they've been doing a fantastic job."
It is McLaren's 62nd front row sweep in Formula One — a record for the sport. It is also the team's third all front row this season.
"It's fantastic for the team," Button said. "I think the last few races have really shown our strength and qualifying both of us on the front row is great. I don't know if any other team has been able to do that this year.
"We'll start thinking about tomorrow in a little while. Even being on the front row, it's not going to be an easy race here but it's the best place to be."
None of the top three has won at Monza before. Hamilton has a great chance at the fast track as the winner has come from pole position in all but two of the past nine Italian Grand Prix.
However, the 27-year-old is not reading anything into that as he bids for his third win of the season.
"It's not particularly encouraging," Hamilton said. "I think that one that wasn't a winner was me! In 2009. When I was on pole."
On Friday, Alonso endured a suspected engine failure in the first practice and a brake problem and gearbox failure during the afternoon session. His problems seemed to be behind him in the morning, but more technical issues saw him finish over 1.5 seconds behind Hamilton in the final qualifying segment.
"Better it happens today than tomorrow," Alonso said. "There was a break in the suspension and there was nothing we could do. The car was impossible to drive and there was no time to fix the car so we just tried to complete one lap to see if we could maybe overtake one or two cars.
"It's annoying as I drove 1:24.0 in Q2 and normally you can improve by three tenths so it was an easy pole position, I had a good chance as the car was performing well. But the race is long, we need to take the potential of the car into tomorrow's race and hopefully we can recover some positions."
It could be another troublesome weekend for Alonso, who saw his lead over Red Bull's Sebastian Vettel cut to 24 points last weekend after his race was ended following a wild multi-car accident caused by Lotus driver Romain Grosjean at the beginning of the race.
"You have to start with the belief that you can still win," Alonso said. "I have to have that 100 per cent.
"You have to think that luck evens itself out and we've had no luck this weekend."
There will be some consolation for the Spaniard in that Red Bull has struggled as well so far at Monza. Vettel finished outside the top 10 in all three practices, although the defending champion was sixth in qualifying.
Paul Di Resta qualified fourth, but will be pushed down to ninth because of a five-place grid penalty for changing gearbox.
A gearbox is supposed to last five consecutive races under FIA regulations, but the Force India team had to install a new one in Di Resta's car after last weekend's Belgium Grand Prix.
Five-time Monza winner Michael Schumacher, who was fastest in the first practice session, finished fifth. He moves up a place because of Di Resta's penalty, as do Vettel, Nico Rosberg, Kimi Raikkonen and Kamui Kobayashi.