Hamilton dropped to third in a manic first two laps that ended with McLaren’s Carlos Sainz leading, but fought back to crush Bottas’ hopes.
After both Mercedes passed Sainz, Hamilton tracked Bottas before taking the lead on lap 20.
From there, Hamilton dominated to take his 92nd career Grand Prix victory
Hamilton received a standing ovation from the socially distanced crowd, before celebrating with team members and then a long embrace with father Anthony.
Hamilton said he “owed it all” to his Mercedes team, adding: “I could only ever have dreamed of being where I am today.
“I didn’t have a magic ball when I chose to come to this team and partner with these great people, but here I am.
“Everything we do together – we are all rowing in the same direction and that’s why we’re doing what we’re doing.
“And my dad’s here and my step mum Linda, and Roscoe [Hamilton’s dog]. It is going to take some time for it to fully sink in. I was still pushing flat out as I came across the line. I can’t find the words at the moment
His victory, on a humiliating day for team-mate Bottas, gave Hamilton a 77-point advantage in the championship as he moves ever closer to a seventh world title, which would match Schumacher’s other surviving record.
Hamilton had to do it the hard way, cool temperatures and a sprinkling of rain at the start leaving his Mercedes grip-less on its medium tyres on the opening lap, on which he was passed by both Bottas and Sainz.
Sainz, using his soft tyres to great advantage over the medium-shod Mercedes, produced a stellar opening lap from seventh on the grid and passed Bottas for the lead at Turn Five on the second lap.
But once the Mercedes’ tyres were up to temperature, they wasted no time in dispatching the McLaren and disappeared into a race of their own.
Hamilton never let Bottas get much more than a couple of seconds ahead and then after 15 laps started to pour on the pace, setting fastest lap after fastest lap to close in on the Finn and then pass for the lead into Turn One.
Once ahead, Hamilton left his team-mate behind, pulling out a lead of more than seven seconds in the next 10 laps, and continuing to inch further clear over the remainder of the race.
Hamilton extended his lead even further after they made their pit stops, as he was able to get the hard tyres into their temperature window more effectively than his team-mate.
The 35-year-old’s only concern was cramp in the final 10 laps but it did not seem to affect him unduly, and he still crossed the line 25 seconds clear of his team-mate.
It a masterful performance, befitting the monumental nature of his achievement, supplanting Schumacher at the head of the all-time win lists, where the German had been for 19 years.
It was an exciting race on a new track to F1, with overtaking and incident aplenty throughout the field.
Red Bull’s Max Verstappen was third, after slipping down to fifth on the manic opening lap, while Charles Leclerc was impressive in recovering fourth place in the Ferrari after he, too, struggled for grip in the opening laps on the medium tyres and dropped to eighth.
Alpha Tauri’s Pierre Gasly was outstanding in taking fifth, grabbing the place with a lovely move around the outside of Racing Point’s Sergio Perez with two laps to go.
Perez, too, drove a strong race, recovering from a first-lap collision with Verstappen and spin, which required him to stop for fresh tyres and drop to last.
Perez came under pressure from Sainz on the last lap, but was able to hold the McLaren off, with the Renaults of Esteban Ocon and Daniel Ricciardo and Ferrari’s Sebastian Vettel close behind.
Kimi Raikkonen was just outside the points, after an outstanding first lap, rising from 16th on the grid to seventh place on his soft tyres, and then passing Leclerc’s Ferrari for sixth, before the lack of pace of his Alfa told once the race settled down and he began to slip back.