Hamilton produced a masterful drive around the Hungaroring to follow up on his wins with McLaren in 2007, 2009 and again last year.
This triumph, however, will taste extra sweet for the 28-year-old Briton as he has been itching to get back on to the top step of the podium after watching team-mate Nico Rosberg win twice earlier this year.
Hamilton finished 10.9 seconds clear of Lotus' Kimi Raikkonen for his 22nd career victory, with the Finn just holding off Red Bull's Sebastian Vettel over the closing laps to claim second.
After congratulations were expressed over the radio between Hamilton and team principal Ross Brawn, Mercedes' non-executive chairman Niki Lauda summed up the drive perfectly.
Lauda said: "He won the race because he drove sensationally, the best I've ever seen him drive in my life.
"We were not as quick as the Red Bull, but Lewis made it all up with the way he passed people. He was outstanding."
Hamilton's first duty was to hold on to his pole on the long run down to the first corner, which he managed with comparative ease.
Instead, it was Vettel who found himself under attack, from Lotus' Romain Grosjean to his left and Mercedes' Nico Rosberg to his right.
Vettel just did enough to retain second place and instead it was German compatriot Rosberg who suffered, as he twice ventured off the track on the opening lap.
The second occasion followed a collision with Massa, dropping him down to 12th and out of the running for a podium finish, with the German then retiring a few laps from home with a blown engine.
What was remarkable was how Mercedes finally managed to make their tyres work and in incredible temperatures - the highest of the year - as the mercury hit 35 while the track was again 50, as was the case yesterday during qualifying.
Mercedes came into the race fully expecting the worst, particularly after missing out on last week's young driver test where the other 10 teams were allowed to test Pirelli's new tyres.
The high-speed blowouts that occurred during the British Grand Prix resulted in Pirelli opting for a plan that has seen last year's construction being married with this year's compounds.
On the backfoot, Mercedes spent the three practice sessions trying to gain as much data as possible, but even so their run of six poles in the previous seven races was under threat.
Imagine the surprise then, when Hamilton pulled off another one-lap stunner yesterday to clinch his 30th career pole, and three in a row for the first time since he entered F1.
Despite that, Hamilton remarked it would take a miracle for him to win, fully believing his tyres would 'drop off a cliff' - to use F1 parlance - as they have done so often in the heat this season.
There was good fortune along the way because one lap after his first pit stop following nine laps, he wasted no time in passing former team-mate Jenson Button.
When Vettel pitted soon after he too came out behind Button, but then found himself stuck behind the Briton for 12 laps - which was crucial - until his tyres eventually fell away,
That was on lap 25 when Button was also barged out of the way by Grosjean, resulting in a post-race stewards' investigation.
A second inquiry followed soon after for the Frenchman as he was found guilty of 'leaving the track and gaining an advantage' in pulling off what initially appeared to be a superb move on Massa around the outside of turn four.
That ruined all hope of a potential maiden victory for Grosjean, who had to settle for sixth.
That left Hamilton to manage the pit stops and his tyres, although there were two moments of consternation.
The first was when Williams' Valtteri Bottas retired on lap 45, his car parked close to the final turn, and with the marshals slow to clear there was a suggestion a safety car would appear.
Mercifully for Hamilton that did not happen nor did an engine blow out of his own, as occurred to Rosberg resulting in nervous moments on the Mercedes pitwall in the closing stages.
Hamilton, who has equalled Michael Schumacher's feat of four wins at this track, has now moved to within 48 points of Vettel.
"It's an incredible feeling. My team did an incredible job," said Hamilton as he took the acclaim of the crowd on the podium.
"We studied things a lot last night and were hoping the tyres would last. We had no idea it would go that well.
"I was hungry for it today, I was going all out. Usually I get stuck in traffic, but today I was going for every move I could.
"For the last 20 laps it was then about managing the tyres, but this is one of the most important wins of my career.
"To win for Mercedes is a privilege. I really couldn't be happier. I just hope there is more to come.
"We've got to keep working hard and see how the tyres last elsewhere, but if we can come here and make them last anything is possible."
Behind the top three, Mark Webber was fourth in his Red Bull, with Ferrari's Fernando Alonso fifth, the Spaniard now 39 points adrift of Vettel and having fallen a point behind Raikkonen.
Grosjean was sixth, followed by Button, Massa, the second McLaren of Sergio Perez, with Pastor Maldonado 10th, giving Williams their first point of the season.