The British team have won in four of the last five years at the track near Budapest. Hamilton triumphed in 2007 and 2009, Heikki Kovalainen in 2008 and Jenson Button, who qualified fourth, was victorious last year, as well as with Honda in 2006.
Hamilton dominated the two days of practice and took pole with a lap of one minute and 20.953 seconds. Lotus's Romain Grosjean (1:21.366) was second, with Sebastian Vettel of Red Bull (1:21.416) third after pipping Button (1:21.583).
Kimi Raikkonen (Lotus, 1:21.730) starts fifth and the Ferraris of championship leader Fernando Alonso (1:21.844) and Felipe Massa (1:21.900) are sixth and seventh.
Alonso's closest rival in the standings, Red Bull's Mark Webber, is back in 11th after failing to make the cut for the third stage of qualifying. Force India's Paul Di Resta will be next to him in 12th.
It is a third pole of the season for Hamilton, who has failed to score points in his last two outings and is fifth in the championship.
He said: "The mechanics did an excellent job. It is great to finally see the upgrades working and I have been able to put the car where I want to this weekend. We are not saying we are relaxed – we know we have a lot of work to do, starting now."
Button said: "I was much happier with the car in qualifying, but nowhere near as good as my team-mate in Q1. I'm disappointed third place got taken away at the end as the circuit is normally cleaner that side."
Conditions were hot and sunny, in contrast to the last two races, in Germany and at Silverstone, but that did not please everyone. Webber, when asked what it would take to improve his title chances, replied: "Rain."
The Australian added: "I was happy this morning and was quick in Q1 but didn't feel happy on the last set of soft tyres."
Alonso felt the same about the weather, while acknowledging that Webber's 11th-placed start was good news for him. The Spaniard said: "We were not in a position to be as quick as the leaders here. Victory will be difficult for us. We need a strange race or maybe some wet conditions. But at the moment we're happy with sixth."
Vettel, who started this race from the front in 2010 and 2011, did not have things his own way in Q1, where he finished 17th.
The defending champion said: "Through qualifying I think things got better but I knew we only had one set of tyres in Q3.
"I think Romain was within reach but Lewis was a bit too far away today. With the progress we've made this morning we should be in a good position in the race."
Di Resta, 13th in the drivers' championship, said: "I think there was more potential in the car today, but I couldn't get the lap time when it counted during Q2. The main issue was trying to find track position and I had to push very hard on my out lap to make some space, which probably took too much out of the tyres.
"It's a shame because we were very quick in Q1 and the car has been working well here. We can still have a good race, but it won't be easy with the high temperatures and the fact that it's never easy to overtake here."