Speculation about Hamilton's future and a possible switch to Mercedes dominated the weekend, but the 2008 champion put the focus firmly back on his driving with his first victory at Monza and the 20th of his career.
"It's a fantastic win in front of the best crowd. I'm happy for the team. It's been the best day," said Hamilton, who started on pole and led almost from start to finish. "It was pretty trouble-free, I don't think I had any problems throughout the race and the guys did a great job through the pit stop. And I got a good start for once, so very, very happy with that."
Hamilton made it three wins in a row for McLaren and moved past defending champion Sebastian Vettel to take second place in the drivers' standings, 37 points behind Alonso. It could have been a perfect day for McLaren, but Jenson Button — who started second and looked on course to finish right behind Hamilton — was forced to retire on the 35th lap.
Alonso started from 10th on the grid after he had technical difficulties during Saturday's qualifying. However, the Spaniard took advantage of a wretched day for Vettel and the Red Bull team to storm his way through the field, much to the delight of the fans at Ferrari's home track.
"It was a perfect Sunday for us," Alonso said. "After the problem yesterday it was not easy to think about victory. So if you are not going to win the podium is the next target.
"All the simulations and predictions said we would never finish on the podium. So it was much better than expected and Jenson was out of the race and so were the two Red Bulls, so the perfect Sunday ... the race went like a movie for us, like a dream."
Vettel had to retire because of a mechanical problem when wisps of white smoke started to emerge from his car with six laps to go. He was joined on the sideline by Red Bull teammate Mark Webber, who retired at the end of the penultimate lap.
Sergio Perez, who revealed he had been feeling sick all weekend, was second on Sunday, 4.3 seconds behind Hamilton after starting 12th. The Mexican finished strongly, moving through the field in the closing stages and cutting into Hamilton's lead, after leaving it until lap 29 to pit and change to softer tires.
"That was a great race for me for my team. It's unbelievable to get a podium in Monza. It's really special," Perez said. "It was really enjoyable. One of those races where you have the pace and you are the one attacking.
"To go that long (before pitting) and to be able to keep the pace was not easy at all. I did quite a lot of laps on those tires. Then in the second stint we managed to go maximum attack and I was able to have good fighting with some drivers. It was just a great race."
Alonso made up three places on the first lap from 10th, and was up to sixth by the second lap.
"Yeah, the start was good," he said. "Obvious we didn't have maybe the best start but it was enough to overtake two or three cars, good first corner and then those two first laps were, I think, making the difference of our race.
"We overtook di Resta, Kimi, Michael very quickly. And that gave us the opportunity to follow Sebastian and the quick cars that were there in the first five positions. So, when you find yourself sixth after two or three laps, the race improves a lot."
A tremendous tussle with Vettel halfway through the race forced Alonso onto the grass adjacent to the track to avoid a collision, with the German later being issued a drive-through penalty.
Ferrari driver Felipe Massa finished fourth after starting third. The Brazilian got off to a strong start, overtaking Button and almost moving past Hamilton on the outside just before the first chicane.
Hamilton managed to hold his old rival at bay, only losing the lead briefly to Perez, who only pit-stopped once.
Button overtook Massa to regain second position shortly before their pit stops and it seemed as if a McLaren 1-2 was on the cards after the team had achieved a record 62nd front-row sweep in qualifying.
One week after giving himself an outside shot at the title with victory at the Belgium GP, however, Button endured a fuel pressure problem and had to quit the race.
That allowed Massa to move into second place but, with Alonso catching him, he allowed his teammate to overtake.
A new threat soon appeared as Perez put in a number of lightning-fast laps. He overtook the Ferrari duo to claim his third podium of the season — and his career.
Alonso finished 20.6 seconds behind Hamilton. Massa was a further 9 seconds behind, just ahead of Kimi Raikkonen and five-time Monza winner Michael Schumacher.