The British driver fought back from a poor start and an even worse safety car restart at the beginning of the race to take his 97th career F1 win.
After reclaiming second from Red Bull's Max Verstappen with a move down the start-finish straight, the seven-time champion netted the lead when he went around the outside of Bottas at turn one on lap 20.
The duo narrowly avoided contact before Hamilton sauntered to a 29-second gap over championship rival Verstappen, who finished second.
Commenting directly after the race, Hamilton said: "That was such a tough race, physically and mentally just keeping everything together.
"It was very windy out there so it was very easy to put a foot wrong. I just didn't quite get as good a start as Valtteri and then I lost out on the restart which was not good, I was not happy with the restart at all.
"I really had to position myself the best I could. I think Max made a mistake at some point during the lap so I knew that was going to be the lap that I would be as close as I could to him in the last sector.
"With Valtteri, I knew I had to make the move early on before the tyres were destroyed and I managed to just get him into turn one, right on my limit. It was a great race."
Hamilton insisted there would be plenty of work to do in the week leading up to the Spanish GP in order to keep Red Bull at bay.
"We have to debrief, we have a lot to download from today and improvements we can make," added the seven-time F1 champion.
"Today wasn't perfect so we will look at those areas and try to turn over the stones."
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