With this victory, Hamilton increased his lead in the driver's standing to 24 points.
The two Mercedes made ideal getaways, Hamilton streaking clear and Bottas staying close to resist attacks as Vettel swept inside into third.
Despite being beaten at the Hungaroring, a track at which Ferrari was expected to comfortably beat Mercedes, Arrivabene has praised the team and its drivers.
That came on lap 65 of the 70-lap race when Vettel finally passed Bottas, the Finn's right front wing touching his rear left tyre under braking, wrecking Mercedes' hopes of a one-two finish.
Hamilton's win was the ideal way to finish the first part of the season but that doesn't obscure the fact that the title race could still go down to the wire.
"We've definitely had ups and downs in this championship, it's such a roller coaster ride", he said.
"Without that it would have been a much more relaxed last part of the race, probably hunting down Lewis".
However, fierce Vettel fought back in Canada and followed by Hamilton in France.
A virtual safety auto after McLaren's Stoffel Vandoorne retired briefly raised Ferrari hopes but no further drama unfolded until Vettel managed to overtake Bottas five laps from the end.
"It was, from my standpoint, it was his best race so far with Mercedes in the last years".
"We came here knowing that the Ferrari would be really quick this weekend", said Hamilton. All good. We'll keep pushing! The season resumes in Belgium on August 26.
"I got hit from behind [by Bottas], I was not sure what had happened and I was lucky the vehicle was not broken and we could carry on".
Asked if "wingman is what you have to accept, driving for Mercedes", he replied: "I think we need to speak after this race, we are over halfway of the year and the points gap is big, so for sure the team will decide at some point". However bad luck now hit the German as he crashed from P1 with just 25 laps to go. By half race distance on lap 35 he was almost 25 seconds behind Vettel.
"So, I am confident that we can improve and it should be a very exciting second half to the season". Vettel's speed was good as he approached his stop; Bottas's didn't seem to be enough.
Vettel said he was not concerned, either by his championship position or by comparisons with a year ago.
"I think what we did was OK but as it turned out with the circumstances we lost out and we came out behind".