The 23-year-old German steered his Red Bull car from pole position to the chequered flag to win ahead of McLaren's Jenson Button, the 2009 champion, and Nick Heidfeld who finished third for Renault.
Vettel's second start-to-finish win in two outings this year came despite further problems with Red Bull's faulty Kinetic Energy Regeneration System (KERS) which gave his team-mate Mark Webber a nightmare start.
The Australian dropped from third to 10th before storming back to finish fourth ahead of the two Ferraris of Brazilian Felipe Massa and two-time champion Fernando Alonso.
Alonso suffered damage to his car in a late charge for the podium when he collided with the rear of Briton Lewis Hamilton's McLaren, suffering a broken front wing that required a pit stop.
Hamilton, the 2008 champion, looked set for a podium spot but finished seventh after a slow pit stop and then a struggle with worn tyres in the closing stages.
Japan's Kamui Kobayashi of Sauber was eighth ahead of seven-time champion Michael Schumacher, who was ninth for Mercedes. Tenth-placed British rookie Paul Di Resta who scored another point for Force India in only his second start.
Vettel has now won both of the two season-opening races in Australia and Malaysia and five of the last six to take charge of the 19-stop drivers' world title race.
It was another stunning performance by Vettel as Red Bull team told him and team-mate Webber they could not use the KERS power-boost for most of the race.
"In the heat, we kept our heads cool," he told the Red Bull crew on his victory lap. "It is a pleasure every week to drive with you boys and I'm loving it."
German Nick Heidfeld finished third for Renault after a dazzling start when he shot from sixth in the grid into second place behind Vettel.
On another hot day, the track temperature was 31 degrees (88 fahrenheit) at the start in 83 percent humidity, a sure sign that rain was likely as Vettel led the cars on the formation lap to the grid.
Vettel made a smooth start, pulling clear of the pack as Hamilton, on the dirtier side of the circuit, struggled to retain second place and, running into turns one and two, was passed on the outside by Heidfeld.
At the same time, Webber was beset by problems. His car has suffered a pre-race KERS failure and this made him slow off the start, dropping seven places.
Webber was first in for new tyres after 11 laps and was followed by Hamilton, who was nine seconds behind Vettel when he pitted.
Heidfeld suffered a slow stop as did Massa and this enabled Button to gain a place while Petrov and then Alonso enjoyed brief spells as leader.
Webber swiftly set about making up ground and set the fastest lap, as did Hamilton and then Alonso soon.
But by lap 20, Vettel was back in front ahead of a chasing Hamilton, Alonso and Button, with Heidfeld back in fifth and Massa sixth before the second round of pit stops.
At the back end, there were already five retirements including the two Williams cars of Rubens Barrichello and Pastor Maldonado, Jarno Trulli of Lotus, Indian Narain Karthikeyan of Hispania and Sauber's Sergio Perez.
Hamilton pitted for a third time on lap 37 and, after a slow 6.9-second stop due to a 'sticky' front left wheel, he rejoined sixth. His frustration grew when team-mate Button pitted faster to gain vital seconds and emerge in front.
When Vettel and Alonso pitted after lap 41, they rejoined in first and fourth positions with the two McLarens between them, leaving all four men with a 15-lap run to the flag on hard tyres.
Alonso attacked Hamilton and the Briton defended grimly until lap 46 when the Spaniard attempted a passing move and brushed the McLaren's rear right tyre.
The collision as they exited turn three left the Ferrari with a damaged front wing that required a pit stop and left Hamilton in clear air in third place, but struggling for pace on his final, used set of tyres.
Heidfeld, as at the start, then closed the gap and passed the struggling Hamilton on lap 51. Webber then overtook Hamilton who pitted for a fourth time and fell down the running order to eighth.
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