The 2008 world champion, who started from pole position, was largely untroubled throughout as he registered his first points of the season after retiring in the season-opening Australian Grand Prix.
Nico Rosberg, Hamilton's teammate and the victor in Melbourne a fortnight ago, finished second to confirm Mercedes' superiority over the rest of the field, with reigning world champion Sebastian Vettel rounding up the podium positions.
Fernando Alonso finished fourth after disposing of Nico Hulkenberg, whose Force India adopted an unorthodox two-stop strategy, late on.
Jenson Button held onto sixth after a team-orders scuffle broke out at Williams in the latter stages of the race, with Felipe Massa ignoring the team's request to let Valtteri Bottas, who was on fresher tyres, to attack the McLaren.
Kevin Magnussen and Daniil Kvyat, the wonderkids of Melbourne, rounded out the points-scoring positions. The former was embroiled in an early incident with Kimi Raikkonen, which forced Magnussen to soon change his front wing and gave the Ferrari driver a race-ruining puncture.
Daniel Ricciardo was among the race's seven retirements after a horror pitstop dropped the Red Bull driver, who was disqualified from his home race two weeks' ago, from fourth to 14th. The Australian's front wing failed a matter of laps later before he boxed for the final time on the 49th of the 56 laps.