Webber took the lead early in the race as he jumped Vettel in the pits, and the Australian then led for most of the race.
But with both cars' tyres and fuel running dangerously low the team ordered the pair to back off and cruise to the end of the race - but Vettel simply ignored the directive, going wheel-to-wheel with his team-mate through a series of corners and overtook him late on.
In a race which will live in the memory for some extraordinary inter-team conflicts, Lewis Hamilton finished third - but only because Mercedes ordered the faster Nico Rosberg to back off, for the same reasons as Red Bull had told its two drivers to stop racing.
The race was punctuated by a series of radio exchanges, with Vettel complaining that "we have to get [Webber] out of the way - he's too slow".
And as the pair jousted for position, against the team's instructions, Vettel was told by Red Bull team principal Christian Horner not to be silly.
"You looked like you wanted it bad enough," the message came through to the world champion after he took the chequered flag, "but still, there'll be some explaining to do."
Webber was clearly furious on the podium, shunning his team-mate during the traditional champagne spraying, complaining that "Seb made his own decisions today."
He added that he had changed his car's engine settings as part of the team orders to conserve fuel and tyres when Vettel decided to overtake.
Vettel later apologised to Webber for his shocking move. "I messed up today - I apologise for that," he said; but as the old saying goes, it's easier to ask for forgiveness than permission.
Mercedes star Hamilton took third - despite an accidental stop in the pits of former team McLaren - but that was equally controversial as team-mate Rosberg was involved in a protracted discussion over the radio with team principal Ross Brawn about letting him through because he felt he was faster.
A clearly embarrassed Hamilton admitted on the podium that, "Nico should be up here instead of me".
Felipe Massa recovered from a horror start to seal fifth place, while his team-mate Fernando Alonso's race ended after a single lap when his damaged front wing collapsed under his wheels and forced him to slide off into the gravel.
The Lotus pair of Romain Grosjean and Kimi Raikkonen were sixth and seventh, Nico Hulkenberg and Sergio Perez picked up their first points for Sauber and McLaren respectively, and Jean-Eric Vergne grabbed the last point for Toro Rosso.
Jenson Button, who had been running well in fifth, had his work undone after a pit error fitting his front-right tyre effectively ending his race.
The drama was expected to come from the weather - showers hit Sepang half an hour before the race started, forcing the field on to intermediates. But by the time the race began the track was already drying and the weather stayed clear for the rest of the afternoon.
Instead it came through team orders, with a furious Webber scarcely able to disguise his contempt at Vettel passing him.
He had begun brilliantly, a rare flying start seeing him race through to second place, which then became the lead after Vettel chose to switch to slick tyres too early and lost position.
"After the last pit stop," Webber said in the press conference on the podium, "the team told me that the race was over and we turn the engines down and we go to the end. I won the race as well, but in the end the team made a decision - we always say before the race: 'Look after the tyres and get the car to the end'.
"In the end Seb made his own decisions today, he will have protection as usual and that's the way it goes."
Hamilton, meanwhile, appeared sheepish despite collecting his first podium place with his new team: "I really feel like Nico should be standing here."
Rosberg doubtless agreed - he begged Brawn to let him race Hamilton, saying "I can go so much faster."
Brawn firmly rejected his pleas, but still the German, who has been friends with Hamilton since their days in GP2, refused to drop back into clean air, as if protesting.
"Remember this one," Rosberg told his team as his race came to an end. Neither he nor the spectators are likely to forget it.