Hamilton's team mate Valtteri Bottas was fourth fastest, ahead of the Red Bulls of Daniel Ricciardo and Max Verstappen, who dominated the first practice session on Friday but were more than a second slower than the Ferraris on Saturday.
"That felt like magic", said a delighted Hamilton of his storming lap record, which was an astonishing 3.4 seconds quicker than last year's pole effort. "Through Q2, Q3, find a second if not more and we just stayed as a stalemate and I don't know why we were the only ones who couldn't find the time right now".
"It was just perfectly to the limit".
The duration of the race, with each of the 61 laps of the 5.063 kilometre track having 23 bends and 80 gear changes - more than any other on the Formula One calendar - means that drivers and machinery are worked to breaking point.
In qualifying yesterday. Lewis Hamilton and Mercedes were wary of Ferrari's straight-line speed going into this race weekend, and that brilliant lap that secured him pole position was just a touch unexpected, particularly after last year's P5 start.
The 20-year-old apologized to his team on the radio as he left his vehicle stranded in an escape road with two minutes left in the session, a sight that will disappoint his future employers, who will hope he does not make similar mistakes next season.
"Honestly this feels like a victory". "We just have to make sure we have a clean start and then everything is possible".
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After the match , Djokovic brought the subject up again with reporters. "For me it's not something that I have to think about. Williams was outraged, and demanded an apology, telling Ramos that "I don't cheat to win, I'd rather lose".
He said: "We tried to be aggressive in the beginning, and it didn't work out".
"It was a messy qualifying session and there was too much time missing so we didn't get any better than third", he added.
Red Bull driver Max Verstappen was nine seconds back in second place, with Vettel way back in third.
Vettel's pass on Verstappen into Turn Seven on the first lap came just before a safety auto was called after Force India's Sergio Perez pushed his team-mate Esteban Ocon into the wall on the exit of the first chicane.
Hamilton admitted that Mercedes had been too conservative in their tyre choices for the race and after sneaking through the first phase of qualifying on the slower ultrasoft tyres, the Briton was unstoppable with the high-grip hypersofts on his vehicle.
And Ferrari's decision to put the German on the faster-degrading ultrasofts while his rivals all swapped to durable soft tyres did little to lower his blood pressure. As we'd gone through the qualifying session again, the real challenge in Q1 on the ultra-soft, and then we obviously got into that last session and it was just about pulling all of the little bits you'd found through practice and trying to see if you could put it into a ideal puzzle.