Mercedes looked set for a one-two finish until both race leader Hamilton and Valtteri Bottas suffered tyre failures.
Bottas’ struck with two laps to go, which saw him finish outside the points, while Hamilton was able to hold on after a puncture at the start of his final lap.
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"Your heart drops," Hamilton told Sky Sports afterwards.
"Up until then everything felt relatively fine. I heard of Valtteri's tyre going and I'd looked after mine relatively well. I backed off a bit and didn't push through the right handers.
"I am so grateful the tyre did not deflate through a high speed corner. It would have been a disaster.
"I nearly didn't make it through the next two corners but rather than panicking I thought how do I get this home. As I started to accelerate the tyre deflated more and I was concerned I would lose the wing and the wing would go under the car. I made some switch changes and just tried my hardest to get round.
"I could hear the seconds being counted down as Max Verstappen was catching me. Thankfully, with support, we managed to bring it home.
"Survival instincts come over you. Right to the limit."
Hamilton led second-placed Max Verstappen by more than 30 seconds heading into the final lap but finished with just a five-second advantage.
"I nearly didn't get around the last two corners, but thank God we did," said Hamilton. "In my mind I'm thinking 'Okay, how far is it to the end of the lap?'
"Bono [race engineer Peter Bonnington] was giving me the information of the gap. I think it was 30 seconds at one stage and it was coming down quite quickly.
"But the car seemed to turn okay through Maggots and Becketts, thankfully. I got to 15 and that's where it really was a bit of a struggle. I could hear the gap coming down from 19 to 10. I thought I would just give it full gas out of 15 down to 16, and then the thing wasn't stopping.
"I got to the corner, a lot of understeer and I heard him go 'nine, eight, seven...' I was like, just get back on the power and try to get the thing to turn.
"You may or may not be surprised but I was really chilled for some reason at the end. I've definitely never experienced anything like that on the last lap. And my heart definitely probably nearly stopped. I think that's probably how cool I was - because my heart nearly stopped!"
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