Hamilton, 36, used his driving and passing skills, as well as his strategic thinking in the rain, to return from seventh place in the first round to a historic victory.
He is the first driver to reach 100 victories.
It was his fifth win of the season and his first since the British Grand Prix in July.
“It took a long time to get to 100 and sometimes I wasn’t sure that would happen,” said the British driver.
“It’s a magical moment. I could only have dreamed of being here again, of having this opportunity to win these races and to drive with such phenomenal talent so late in my career. “
“I’m so proud of everything we’ve done with Mercedes, on and off the track, and it’s a special moment for everyone who’s been there.
“My dad called me last night and he’s always been the one to reassure me and continue to support me. I am incredibly grateful for the incredible support I have received. “
The victory puts Hamilton two points ahead of Max Verstappen in the title race with seven rounds to go.
It also deprived Lando Norris of his first victory after an exciting final.
Norris, 21, looked set to keep Hamilton at bay and become Britain’s youngest Formula 1 winner.