"That felt like magic," said Hamilton of his lap record, which was 3.4 seconds quicker than last year's pole effort.
"It was really special,” added the 33-year-old Briton. “I don't think there was a bad moment in the lap, it was just perfect.
"I don't know where it came from but it all came together. It's one of the best laps I can remember."
Ferrari's Vettel, who is 30 points behind Hamilton in the title race with seven races to go, said he was disappointed with his best effort of 1 minute 36.628 seconds.
"It's not ideal obviously. We wanted to get pole and didn't," said the German. "It was a messy qualifying session and there was too much time missing so we didn't get any better than third," he added.
Hamilton's teammate, Valtteri Bottas, finished the qualifying rounds in fourth place and Kimi Raikkonen will start Sunday’s race in fifth in the second Ferrari.