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," Hamilton said.
It's unlikely to have much impact on the championship after an impressive race from Alonso, much to the delight of the fans at Ferrari's home track. The Spaniard started from 10th on the grid after he had technical difficulties during qualifying.
Hamilton moved past defending champion Sebastian Vettel to take second place in the drivers' standings, 37 points behind Alonso.
"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."
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.
Jenson Button was forced out of the race on the 35th lap just when the McLaren driver was looking on course for second place.
Sergio Perez 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.
"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.
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.
Alonso made up three places on the first lap from 10th, and was up to sixth by the second lap.
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.