The Briton claimed a pole-to-flag victory ahead of teammate Nico Rosberg in a first Mercedes one-two since they returned to Formula One as a works team in 2010.
The 2008 Formula One world champion easily pulled away from his rivals on a dry track with a three-stop strategy to win the race by 17.3 seconds, his 23rd career victory and first in Malaysia at the eighth attempt.
"Incredibly happy, it's my eighth year here (at Sepang) and finally I got that win," the Briton told reporters after taking the chequered flag for his second win for Mercedes since he joined them last year and first points of the season.
"Its quite special to get a one-two, I haven't had many in my career, so that makes it even more special. A great day," added the former McLaren driver.
Rosberg, who won the season opener in Australia two weeks ago, started in third place but squeezed past quadruple world champion Sebastian Vettel into the first corner and was able to keep the Red Bull at bay and stay top of the driver standings.
It was Mercedes' first one-two since 1955, their last year as a works team before 2010.
Rosberg almost touched the wall as he took Vettel at the start and struggled to manage his rear tyres in the early stages as the two Germans remained close before the Mercedes driver pulled away over the closing laps.
The second place finish moved him on to 43 points in the standings, 18 clear of Hamilton with Ferrari's Fernando Alonso third on 24 points after his second fourth of the season.
Mercedes took the lead from McLaren in the constructors' standings.
"I had a really good start.. got away well and I thought Sebastian was going to put me into the wall but he stopped just before so thank-you for that," Rosberg said.
"My heart skipped a beat a little bit but it was OK. I was trying to chase Lewis but he was a bit too quick today."
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