The German overtook polesitter Nico Rosberg on the third lap and never looked back, winning by 10.9 seconds from Lotus duo Kimi Raikkonen and Romain Grosjean - an identical podium to 2012.
Vettel avoided the carnage of an eventful race enlivened by severe tyre degradation in the Sakhir heat. McLaren's Jenson Button and Sergio Perez became the latest pair of team-mates to go toe-to-toe, as the Mexican's robust attempts to overtake his colleague resulted in contact.
Button was heard on his team radio instructing McLaren to calm Perez down, before telling them in no uncertain terms to "sort it". Perez eventually won out, coming sixth with Button a disappointing 10th.
Force India's Paul Di Resta narrowly missed out on the first podium finish of his career - the Scot lost out to Grosjean late on and had to settle for fourth.
Lewis Hamilton took a creditable fifth despite Mercedes suffering serious tyre problems, while Rosberg endured a miserable race, dropping from pole position to finish ninth.
Fernando Alonso made the best of a calamitous weekend for Ferrari, finishing eighth despite making two unscheduled trips to the pits and having no DRS after an early failure. Felipe Massa, meanwhile, came 15th after suffering a puncture.
Vettel's second win of 2013 moves him 10 points clear of Raikkonen in the driver standings, with Alonso now 30 points behind the reigning champion.
Vettel was in a hurry to hit the front from the outset.
Alonso was soon up to second but his DRS flap jammed open. He made an emergency pitstop to fix it, but the problem reoccurred. By lap nine, he was 19th, had made two pitstops and knew he would be without DRS all afternoon.
With Alonso out of contention, the best of the rest battle became a contest between di Resta and Raikkonen, both two-stopping compared to most frontrunners' three.
Di Resta looked to be best-placed to win the battle until his final stop, when Raikkonen vaulted him having stopped sooner.
Force India remained on course for third for a while, but Grosjean was looming. The three-stopping Frenchman saved his medium tyres for the final stint and was able to hunt down and pass di Resta, who had to settle for a career-best fourth.
The rest of the top 10 featured wild racing all afternoon, with an abundance of side by side and wheel to wheel action as different strategies unfolded and different cars found pace at different junctures.
Perez produced by far his most combative performance for McLaren yet. He was embroiled in a long dice with team-mate Button and the fading Rosberg, which featured contact between the McLarens and anxious radio messages on more than one occasion.
"He was too aggressive," Button said of Perez afterwards. "It was a bit of a surprise, and I'm probably not the only one who thinks that."
Despite losing a front wing endplate against his team-mate's car, Perez finished sixth, joining Hamilton in passing Mark Webber on the final lap.
"I was as aggressive as he was with me," Perez said of his part in the battle.
A three-week break follows before the season comes to Europe at the Spanish Grand Prix.