Vettel, who started from the back of the grid after missing qualifying yesterday, displayed blistering pace throughout the race and broke Juan Pablo Montoya's long standing 2004 lap record of 1:34:223s with a 1:34:080s effort.
The victory comes a day after Verstappen's 20th birthday and ends a winless run dating to the Spanish Grand Prix last season, his first since being promoted to Red Bull from Toro Rosso.
Verstappen quickly pulled away, building a seven-second lead within 10 laps and, despite problems with his neck muscles in the closing laps on this demanding track, was always in control.
The luck for Mercedes held - even with a second place for Hamilton - with Raikkonen's Ferrari suffering a similar engine turbo fault before the race started, with Raikkonen not making the starting grid.
"But I didn't see any pace in clear air that they had on the super-soft or soft tyre that was quicker than what we were capable of doing". "I feel positive, the debrief was one of the best debriefs we have had".
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The Dutchman is already the F1's youngest ever driver to win an F1 race at the Spanish GP in Barcelona previous year.
"After a weekend where we have lacked a significant chunk of performance, we couldn't have imagined such a good outcome, but we can't let that distract us from the job we have in front of us", said Wolff.
As Verstappen eked out a lead, Ricciardo was attacking the second Mercedes of Valtteri Bottas for third place.
Hamilton, who now leads the championship race with a 34 point advantage over second-placed Sebastian Vettel, said it was decent result considering issues he faced with his auto.
"Congratulations to Max, said Hamilton". I think we are quicker so obviously it was a bit of a shame.
After what has been described as a hard season, Red Bull Racing's Max Verstappen gave himself the ideal birthday present at the Sepang Circuit today. "You know, especially after the season I've had, I think this victory came at a very good time", said Verstappen, whose father Jos - a former Formula One driver himself - and sister Victoria were moved to tears. Vettel's championship hopes are still alive, though, so it will be interesting to see how he and the Ferrari team approaches the Japanese Grand Prix next weekend.