The 22-year-old German beat Australian team mate Mark Webber by 17.8 seconds under the Yas Marina floodlights to become the first winner in the oil-rich emirate and cement second place in the championship.
"The priority was to secure second place and we succeeded," said Vettel, still sweating with exertion after the sport's first day-to-night race. "To do it with a win is the best."
While Vettel chalked up his fourth victory of the season, Red Bull completed a hat-trick -- having won the previous two races in Japan and Brazil -- and their fourth one-two after starting the year without ever having stood on top of the podium.
Britain's Jenson Button, who clinched the title in the previous Brazilian Grand Prix for his championship-winning Brawn GP team, rounded off his season with third place after hunting down Webber and chasing him nose-to-tail in the closing laps.
A mere 0.6 of a second separated the two cars at the chequered flag.
"It was a great race, I really enjoyed it," said Button. "This race was a bonus for me. I came here to enjoy myself, which is exactly what I did."
