Starting last, the 25-year-old German never doubted he could be a contender after being sent from third place on the grid to the pit lane for a fuel infringement in qualifying.
When asked if he thought a podium was achievable at the start of the race, Vettel said: "Yes I did to be honest with you."
By the end of a chaotic and crash-strewn evening, the double world champion stood on the podium in third place while title rival Fernando Alonso was second for Ferrari behind race winner Kimi Raikkonen.
Vettel's championship lead, which would have passed into the Spaniard's hands had he failed to score, was trimmed from 13 points to 10 with two races remaining and left the German in a position to seal his third title in Texas in two weeks' time.
"He's mentally incredibly strong," team principal Christian Horner said as mechanics packed up around the paddock.
"Before the race I went to see him in his room to wish him good luck and he was in there playing a drum kit with his trainer and he said, 'I'll see you on the podium'.
"He was the one guy in the briefing room last night, while the rest of us were ready to slit our wrists, who was saying 'It's not an issue. We can still do this'.
"It's that mental strength that he has that is one of his biggest assets."
On Saturday evening Horner had addressed reporters at the same place outside the Red Bull hospitality building to outline why his driver had been stripped of his qualifying times and sent to the back of the grid.
He had explained that Red Bull would take Vettel's car out of the sealed 'parc ferme' to work on it, hoping that a points finish might be possible with a more aggressive set-up including different gear ratios and suspension.
Vettel, who had been hoping for a fifth successive win up to that point, had merely quoted Finnish Olympic ski jumping great Matti Nykanen's observation that 'Every chance is an opportunity'.
On Sunday, such was Vettel's speed - coupled with a helping hand from two safety car interludes - that he looked like he might become the first driver to win after starting in last position.
"I said to myself 'Either we go full attack or nothing'," he said after the floodlit day-to-night race around the harbourside Yas Marina circuit.
"I think we can be very proud today. We got the maximum. We lost only a very little bit, I think we have the momentum still and the car is bloody quick."
Surrounded by reporters in the pit lane before the start, and with Formula One supremo Bernie Ecclestone making the trek down to wish him luck, Vettel told his mechanics he trusted them 100 percent.
The start was far from perfect, with the Red Bull suffering some front wing damage that was worsened when he hit a trackside marker board and, pitting for a replacement nose, went to the back again.
"Usually it's hard enough to fight your way once through the field but we did it twice today," said Vettel.
"We were dead last. At least we had a fresh wing and from then went through the field. It was a lot of fun... it was a big chance to lose out a lot today but we didn't lose anything so I'm very happy."
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