With about 10 laps to race, the German came close to snatch the lead at the British, placing himself at her side in a long passage right.
Hamilton and Raikkonen were the first to head out in Q3.
"I'm not entirely happy", said Vettel, adding that he got his approach slightly wrong.
In a gripping season in which neither driver has managed to score consecutive race victories, Hamilton bounced back after Vettel's win last time out in Hungary to cut the Ferrari driver's World Championship lead to seven points. Overall I think the vehicle is there to do the job to go fast.
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Hamilton found even more time on his second Q3 run, clinching pole with a stunning 1m42.553s effort. Hamilton was twice awarded the second position. I was just able to keep them at bay, Hamilton told Sky F1.
"It's going to take everything from every single one of us to finish these next eight races and come out on top, which is how a championship should be so I am actually really looking forward to that challenge, but I need to have strong weekends like this". It has established itself in Azerbaijan, in the month of June.
"It was hard to find the right timing and the right gap", he explained. I was a bit so-so. Having already come into contact on the first lap, the two later had a more violent impact that brought out the safety vehicle on lap 30.
While the roles within Ferrari are well defined, Hamilton returned third place to teammate Valtteri Bottas in Hungary to honour a previous agreement between the drivers.
Max Verstappen headed team-mate Daniel Ricciardo to an all-Red Bull third row. The rivalry between Petronas Mercedes and Scuderia Ferrari is turning out to be one of the best things that could happen to Formula 1. He went 10th, but his McLaren did not give the desired performance. Spa proved that as Vettel was able to stick close to Hamilton throughout the race, whereas it wouldn't have been such a tight contest in races prior.