The Briton took his first win in Mercedes colours in Budapest, converting his third consecutive pole position into a first victory.
The win came despite Hamilton all but ruling out a win after taking pole, his pessimism prompted by Mercedes' tyre woes.
"We hadn't had the test, we were on backfoot when we came in, not expecting it to be on pole and were surprised with that," he said after the race.
"I think this is probably one of the most important grand prix wins of my career. To go to a new team and win with Mercedes Benz is a real privilege, the guys did a great job.
"It is an incredible feeling and my team did an incredible job.
"We studied a lot last night, and hoped the tyres would work for us. [We had] no idea it would go that well, in the last 20 minutes I was managing tyres and cruising.
"I think you could tell I was hungry for it today. I was going all out. I needed to get past those people, usually I got stuck - today I wasn't having it, I was going for every move I had."
Hamilton added that the win was an important step forward to the team, as it looks to improve its use of the Pirelli tyre.
"We have to work hard, you never know how the tyres will last elsewhere," he said.
"[But] if we can come here and make the tyres last, we should be able to do it anywhere."