Hamilton streaked away from pole position and was never pressured as he led a Mercedes one-two with Nico Rosberg which confirmed the German marque's dominance in the new Formula One era.
Four-time defending world champion Sebastian Vettel was powerless to catch Rosberg in his Red Bull and he finished third, with Ferrari's Fernando Alonso fourth and Nico Hulkenberg fifth for Force India.
The win was sweet for Hamilton, who has not topped the podium since Hungary last July and retired early at the season-opener in Australia, setting back his bid for a second world title.
Rain had badly disrupted qualifying but Malaysia's notorious downpours were largely absent as Hamilton took the chequered flag 17 seconds ahead of Rosberg.
Afterwards, he paid tribute to the victims of the mysterious MH370 plane disappearance, which cast a shadow over the race and was blamed for poor ticket sales with the Sepang circuit only about half-full.
"Incredible, incredible," Hamilton said of the win. "I just feel so grateful particularly after such a tragedy three weeks ago. I would like to dedicate it to those people and their families."
After a sombre minute's silence for the MH370 missing, Hamilton got away smoothly from pole as his team-mate Rosberg squeezed inside Vettel and into second position on the starting straight.
Behind the leaders, McLaren's Kevin Magnussen clipped Ferrari driver Kimi Raikkonen's right rear tyre, leaving him with a flat, and Pastor Maldonado crashed with Jules Bianchi.
Hamilton was streaking away in front and he had a 5.2-second lead by lap nine, with Rosberg nearly four seconds ahead of Vettel in third and Daniel Ricciardo fourth in the second Red Bull.
Williams' Felipe Massa and Valtteri Bottas, who was warned over the radio to stop attacking his team-mate, moved up a place when Magnussen had to come in for a stop-go penalty for his collision with Raikkonen.
Hamilton pitted after lap 15 and rejoined behind Force India's Hulkenberg, who had yet to make his first stop, and he quickly regained the lead with an eight-second advantage over Rosberg.
Mercedes' relaxed instructions to Hamilton were "just keep doing what you're doing" as the former world champion extended to a 10-second lead by halfway and with Rosberg comfortably ahead of Vettel.
As rain started falling on parts of the track, the two leaders were the last to come in for their second pit stops and Hamilton regained with a healthy 12-second lead.
Red Bull reported trouble with Ricciardo's fuel sensor but then disaster struck the Australian as after his third pit stop, he drove off with a loose front left wheel and had to go back to the garage.
It got worse for Ricciardo, disqualified from second place for a fuel sensor issue in Melbourne, when his front wing came loose and he had to return to the pits again, finally rejoining in 16th.
And the officials compounded the misery of the troubled Australian when they pulled him in for a 10-second stop-go penalty for the unsafe pit stop release. He retired before the finish.
Behind the top five, Jenson Button was sixth for McLaren and Massa finished seventh, ahead of Bottas despite team instructions ordering him to let his team-mate pass.
Several drivers wore helmet stickers reading "Pray for MH370" and the Malay-language "Doa Untuk MH370" after 239 people were presumed killed in the missing Malaysia Airlines jet.