The Mercedes driver finished 24 seconds clear of Max Verstappen and 44 seconds ahead of teammate Valtteri Bottas in a crushing performance at Sunday's Spanish Grand Prix to extend his lead at the summit of the world championship.
Hamilton is now 37 points clear of Red Bull driver Verstappen.
While Hamilton's 88th career victory moved him to within just three of Schumacher's all-time win tally - one he could now match at Ferrari's 1,000th Grand Prix in Tuscany on September 13 - he also toppled the German's record podium finishes.
No driver in Formula One's 70-year history has stood on a grand prix rostrum more times than Hamilton's stunning 156 visits from 256 starts.
"We all grew up watching Michael and dreaming of one day being here," said Hamilton. "What is happening right now is far beyond what I dreamed of as a kid and I am incredibly grateful for the opportunity that I am given every day.
"Michael was an incredible athlete and driver so I just feel humble and honoured to be mentioned in the same light as a driver like him, like Ayrton Senna and like Juan Manuel Fangio, too. I hope the Hamilton family are also proud."
Hamilton will head to the seventh round in Belgium a week on Sunday knowing that a win there, and then in Imola a week later, will provide him with the opportunity to equal Schumacher's 91 victories - the last of which he recorded in China in 2006 - at Ferrari's home track in Mugello. The Briton remains comfortably on course to equal Schumacher's seven titles this season, too.
The 35-year-old is the sport's sole black driver and he has already said that winning the championship alongside his personal fight against racism will rank as his greatest achievement.
Hamilton, who has taken a knee before every race this season, pointed towards the Black Lives Matter logo on top of his helmet as he celebrated Sunday's thumping win.
"Lewis has always been at his best when fighting adversity, and the Black Lives Matter movement is close to his heart," said Mercedes team principal Toto Wolff. "So, it certainly helps him in terms of motivation.
"I am always impressed with how Lewis develops every season. He gets better, in terms of his personality, his driving, and that is really inspiring.
"As a man in his mid-thirties, he is able to show how you can develop as a personality, how you can improve your game, and how you can have interests outside of motor racing that make you stronger."
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