The Brit's fourth-place finish in Mexico was enough for Hamilton to equal the great Juan Manuel Fangio's record.
But after the dust had settled over his achievements, Hamilton turned his attentions to Davidson who he described as the "godfather of the family."
Speaking after his win, Hamilton said: "This has actually been a really difficult weekend because my grandad died on Thursday morning,
"My grandfather would be so proud of us, so grateful that the Hamilton name is established and that it will now go down in history, which is kind of crazy to think.
"Naturally when someone passes away it brings the whole family together but he was the godfather of the family."
Davidson, believed to have been 88, emigrated from Grenada to London in 1955 and worked for London Underground.
Hamilton may have been reflective in his celebrations after he took a flight to his Los Angeles home to spend time with his two dogs Roscoe and Coco.
The 33-year-old then spoke about his father, Anthony, who introduced him to go-karting at a young age.
He added: "My dad and I were already quite close, but this death has made us even more so. I will never forget the things that he did in order for me to be here today and for us to thrive.
"I really do aspire to be like him, as a strong black man, and as a father for doing what he did in the difficult times, with what little he had. I think that's testament to where we are."
Hamilton is now just two world titles away from equalling the great Michael Schumacher's record.
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