"What a attractive day, what a great auto", said Hamilton, who won by 17 seconds.
That left Bottas able to manage his own race, while up front Hamilton was able to extend his Ultrasoft stint through to lap 25, at which point he had established an 8.6 second lead over Vettel. He got in front of Bottas who then ran into the back of Vettel damaging his front wing.
After the race in Hungary, Hamilton said Mercedes held the lead of the title race because, even if Ferrari had the quicker auto, the Silver Arrows had "operated better and been better on strategy". "It's not easy. It's better if you start from first, but we're starting from fourth so we're focussed on winning from fourth". "But I think all around, as a whole, we have hopefully done a slightly better job".
"I don't believe there's ever a moment that you've got your hands on the title or the trophy". We've got a long, long way still to go and there's still nine races. All good. We'll keep pushing!
After 12 races, Hamilton has 213 points to Vettel's 189.
Ferrari was lapping up the compliments about having the quickest vehicle on the circuit and Vettel seemed in the ascendancy after taking a superb pole in Germany.
"This year has shown so far that our auto is more efficient, our vehicle is stronger and still has a lot of potential to unleash", Vettel said. "This year has shown our vehicle is more efficient, our auto is stronger and still has a lot of potential to unleash".
The Briton has now won six times in Hungary, more than any driver, but has yet to do so and take the title in the same season.More news: Mars to reach closest point to Earth since 2003
"Without his great drive the team may not have won today", Hamilton wrote on Instagram after the race.
After Saturday's rain-lashed qualifying, the teams had a free choice of tyres, which saw Ferrari split their strategy - Vettel, like Sainz, choosing softs, while Raikkonen and the rest started on ultra-softs.
We are on equal terms and I trust the team 100% on that.
Wolff was speaking to television reporters after the race when he said Bottas "deserved a podium because he was such a sensational wingman".
But Wolff defended his remarks about Bottas, and said they had been misinterpreted.
Referring to reports of Bottas's reaction, Wolff said: "That's exactly why things that are not being discussed directly face-to-face are being completely spun out of control in the wrong way". "I have not called a meeting with the bosses for Toto saying I was the ideal wingman in this race".
"It was, from my standpoint, the best race so far with Mercedes in the last three years", he added.