Colombian Juan Pablo Montoya [ Images ] finished second for Williams, and also set the fastest lap, while Briton Jenson Button [ Images ] collected the first podium of his Formula One career in third place for BAR.
It was Schumacher's 72nd career win, his second in two races this season and third in Malaysia.
"It was pressure all the way," said Schumacher, whose words will do little to allay fears that the sport is heading for a rerun of Ferrari's 2002 domination. "In the moments when we needed to be quick, we were quick enough."
He leads the championship with 20 points ahead of Brazilian team mate Rubens Barrichello [ Images ] with 13 and Montoya on 12.
Ferrari lead the constructors' standings with 33 points to Williams' 17.
Button was the feel-good story of the day, sprayed by champagne by both Montoya and Schumacher on his first trip to the podium.
"It's amazing," he said. "It's obviously not the pinnacle of what we want but it's a step in the right direction. I'm ecstatic."
Despite Schumacher's success, winning from pole position, Ferrari were less dominant than they had been in the one sided season-opening Australian Grand Prix when he and Barrichello finished one-two.
Last year's championship challenger Kimi Raikkonen [ Images ], in a McLaren, retired 15 laps from the finish after suffering his second engine failure in two races.
An appalling start by Jaguar's Mark Webber [ Images ], making his first front row appearance, shook up the field into the first corner on a slippery track after a sudden shower just before the formation lap.
The Australian plunged from second place to 14th in the blink of an eye before moving back up to ninth by the end of the first lap.
It was the start of nightmare afternoon for Webber, who shredded a tyre on lap five and then collected a drive-through penalty for speeding in the pitlane. Lapped by Schumacher, he skidded out before the halfway point.
Alonso, meanwhile, was on a charge, roaring past five cars at the start to move up from the back row of the grid to 14th place as Schumacher and Barrichello adopted the familiar Ferrari one-two.
Within four laps the Spaniard, with a black ribbon painted on the side of his car as a mark of mourning for the recent Madrid bomb victims, was running in the points.
A mistake by Barrichello on lap two pushed the Brazilian down to fourth place, springing Montoya to chase after Schumacher.
When the German pitted on lap nine, the Colombian became the first driver this season other than Schumacher to lead for a race lap.
Schumacher's younger brother Ralf, the Williams driver who had threatened earlier in the week to force Montoya off the track, was himself dumped out by an engine failure on lap 28.
Raikkonen suffered a similar fate after running in the top three for most of the race.
The Finn, title runner-up to Schumacher last year but without a point in two races, took his second successive engine failure badly and angrily shoved a marshal out of the way as he walked back to the paddock.