Vettel, who won in Canada two weeks ago, has an one-point lead over his fellow four-time world champion.
Hamilton was only fifth in Montreal while Red Bull's Max Verstappen put a series of crash-strewn races behind him to come home third and show he is a class driver when he limits the risks.
Hamilton had topped the times in both of Friday's practice sessions, and then Bottas had been quickest in Saturday's final practice, which was hit by a rain storm.
This was clear evidence not only of Hamilton s pure pace, but also his innate ability to learn a new circuit very quickly. "It is such a lovely place", he added. "It s really stunning down here". Hey, even the traffic jams getting in and out of Paul Ricard last weekend harked back to the good old days...
"There s a couple of places for example on the back straight where you re trying to find out where the corner is and it s really hard to see".More news: Strong Irish economy vulnerable to Brexit
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Hamilton benefited from an engine upgrade that Mercedes failed to roll out in the last round when the British driver lost his lead to Vettel.
"Great work guys! I'm so happy for England as well", he said over the team radio, referring to the national soccer team's 6-1 World Cup rout of Panama in Russian Federation.
"The game will be on TV here and l am sure my guys will try to keep an eye on both things at the same time - as will I".
Q3 was a two part affair after Romain Grosjean wrecked his Haas part way through, but part two was a shootout between Hamiulton and Bottas, and it was the Brit's victory, leaving Bottas in second for a Mercedes front row and Vettel in the Ferrari relegated to third.
The 90-minute opening session was red-flagged with a minute remaining when Ericsson lost control at the Beausset corner, spun and hit the barriers hard, with the Sauber vehicle then catching fire.