Ferrari's Vettel took the chequered flag a comfortable 11 seconds clear at the Spa-Francorchamps circuit to reduce Hamilton's championship lead to 17 points.
Unlike in the wet of qualifying 24 hours earlier, Hamilton was no match for Vettel in the dry conditions with the German driver sealing the win following an opening-lap passing move.
Hamilton held off Vettel on the short dash to La Source, but could not prevent the Ferrari car from sailing past him after the uphill exit of Eau Rouge and on to the Kemmel Straight.
Ferrari are able to deploy more power from their engine than Mercedes, which provides them with a greater advantage on the straights.
"They [Ferrari] have got a few trick things going on in the car so we have got to keep pushing," Hamilton cryptically said in the moments after the race.
Ferrari have been subjected to a series of investigations about their engine by Formula One's governing body, the FIA, this season, but have not been found guilty of any wrongdoing.
Hamilton later added: "We all have trick things on our car, but I guess trick is a word for something special."
Asked if he thought the Ferrari car was legal, he replied: "I don't know what is on their car so I can't tell you either way."
This season marks the first time in the post-2013 hybrid era that Mercedes does not have the best package.
Hamilton's Mercedes boss, Toto Wolff, added: "It is human nature that if you are outperformed on track, you look at yourself, and then you look at your competitors. If you can't find an explanation then you imagine all the nasty things.
"I haven't got any information but I have faith in the [Formula One's governing body] FIA. They are on top of things that control every team. As far as I am concerned the FIA are doing the right things."
Vettel's victory was the 52nd of his career, which moves him ahead of Alain Prost and behind only Michael Schumacher and Hamilton in terms of all-time wins.
Crucially, the result ensures the German is firmly back in the championship hunt following Hamilton's back-to-back wins before the summer break. It is also a timely victory for Ferrari with their home race in Italy to come next week.
"This is a great win for the whole team and I hope in Monza it will be the same," Vettel said. "But we need to keep fighting to always be up there."
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