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.
"In the heat, we kept our heads cool," the jubilant Vettel told the Red Bull crew on his victory lap.
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 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 a struggle with worn tyres in the closing stages.
"It was tough, one of those days for me," said the downcast Briton. "But I have to take it on the chin and get on with it."
Vettel has now won the season's first two races in Australia and Malaysia - and five of the last six - to take charge of the 19-stop championship and establish himself as the outstanding driver of the moment.
Sunday's victory was hard-won in the soaring heat and humidity of Sepang International Circuit, and after Vettel lost the KERS overdrive system mid-way through the 56-lap race.
"It was a lot closer this time than it was in the first race, but we are still just in front," Vettel said. "So we know we have to a lot of work now to stay there."
He said the loss of KERS after 29 laps was "not according to plan" but was relieved his equipment had worked at the start. "It would have been a completely different race otherwise," Vettel admitted.
The German came home 3.2 seconds ahead of Button and 25 seconds clear of Heidfeld, who is deputising for the injured Robert Kubica after a rallying crash and claimed his first podium in two years.
Heidfeld enjoyed a dazzling start when he shot from sixth in the grid into provisional second place behind Vettel.
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.
On a typically steamy day in Malaysia, the track temperature was 31 degrees (88 fahrenheit) at the start in 83 per cent humidity.
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 as his car suffered a pre-race KERS failure and cost him seven places at the start.
"It was a tough race," said Webber. "You get killed on the long runs without KERS and it's tough to clear people."
Vettel moves to 50 points in the drivers' championship with Button second on 26, Hamilton on 24 and Webber on 22.
In the constructors' standings, Red Bull lead with 72 points ahead of McLaren on 50, ahead of the next race in a week's time in China.
Red Bull team boss Christian Horner paid tribute to a nerveless performance from Vettel, who is still only 23.
"I think Sebastian was the coolest guy out there - his composure, the way he controlled the race, the way he looked after his tyres," Horner said.
"We had options to do three or four stops, and he gave us those options - it was a really mature drive.
"We forget he's just 23 years old - he can only just rent a hire car! He's gaining more experience and just continues to get better."