The reigning Formula One champion beat Raikkonen to the checkered flag by nearly 12 seconds after dominating the 70-lap race.
"It's an incredible feeling to be back here after what felt such a long time away and what was such a struggle with me and my team," Hamilton said after his second victory this season and 10th in his F1 career.
This month's winner at the German Grand Prix, Mark Webber (Renault) finished third, Nico Rosberg (Williams) fourth and Heikki Kovalainen (McLaren) fifth.
Felipe Massa (Ferrari) remains in serious but stable condition in intensive care at AEK Hospital in Budapest following surgery late Saturday for a fractured skull.
"The condition of Felipe is stable, and there were no complications during the night," Ferrari team spokesman Stefano Domenicali said before the race.