After crashing out at the first corner of last Sunday's Belgian Grand Prix along with championship leader Fernando Alonso, and amid the saga of his contract negotiations with McLaren, Hamilton conjured a superb drive at Monza to claim his third win of the season and 20th of his career.
The Briton finished 4.3 seconds ahead of Sauber's Sergio Perez in second place, with Alonso giving the Ferrari fans plenty to cheer with third to establish a 37-point gap in the standings ahead of new second-placed man Hamilton.
The start was routine enough for Hamilton, a straightforward getaway, with no drama alongside Button after McLaren celebrated the 62nd front-row lockout, and a new F1 record on Saturday.
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Instead, it was Ferrari's Felipe Massa who proved to be the biggest thorn in Hamilton's side as the Brazilian attacked going into the first chicane, Rettifilo.
Hamilton, however, just did enough to keep his old rival at bay, the duo avoiding a collision after becoming entangled on numerous occasions last season.
That allowed Hamilton to begin his march to victory as he was rarely troubled en route, losing the lead only momentarily when a one-stopping Perez managed to run through to lap 29.
Behind him was another masterclass of a drive from Alonso, who had started 10th in the wake of a disappointing qualifying when - with pole there for the taking - a rear anti-roll bar broke in Q3.
Alonso, however, made up three places on lap one, had moved past Lotus' Kimi Raikkonen on lap two, and soon after was running fifth when he cut his was past Michael Schumacher in his Mercedes.
That left him with reigning champion Sebastian Vettel in his sights, and it was not long before the duo were going head to head.
A failed pass into Rettifilo was soon followed by a brave move through the Curva Grande, one which Vettel defended with too much aggression as he forced Alonso on to the grass.
The stewards took a dim view as they handed the 24-year-old German a drive-through penalty, with his woes compounded later on when he retired along the pit straight with wisps of white smoke coming from his car.
Vettel was the second big-name retirement as hopes of a dream one-two for McLaren were scuppered when Button pulled off track on lap 33 complaining of a lack of drive.
Just a week after thrusting himself back into title contention with his win in Belgium, now 78 points adrift, the 32-year-old would again appear to be out of the reckoning.
Button's exit elevated Alonso to third, which unsurprisingly became second soon after when he eased past Massa, and at that stage two Ferrari drivers on the podium was on the cards.
But Perez suddenly put in a number of lightning laps. First he flashed by Massa - who went on to finish fourth - and soon after Alonso, making no mistake in contrast to Malaysia earlier this year when he threw away the prospect of a win with an error and with the latter in his sights.
If Vettel's retirement was bad enough for Red Bull, worse followed in the closing stages when team-mate Mark Webber dropped three places from seventh to 10th with a spin on to the grass, only to retire in the pits a lap from home.
The upshot leaves Hamilton as Alonso's nearest challenger, with Lotus' Kimi Raikkonen a further point down in third after the Finn finished fifth on Sunday, whilst Vettel is a further point adrift. Webber is now 47 points down overall.
A happy Hamilton said: "It's a fantastic win in front of the best crowd. I'm happy for the team. It's been the best day."
Perez was beaming from ear to ear as he said: "That was a great race for me for my team. It's unbelievable to get a podium in Monza. It's really special."
Taking the bulk of the cheers from the crowd, Alonso was content enough with third as he said: "It was a difficult race starting 10th, but we knew we had the quickest car, so to recover the way we did was good."
The Mercedes duo of Schumacher and Nico Rosberg were sixth and seventh, followed by Paul Di Resta in his Force India, the Sauber of Kamui Kobayashi and Williams of Bruno Senna.