Vettel was forced to start from the pitlane for the Abu Dhabi Grand Prix after stewards found Red Bull guilty of a fuel infringement following qualifying, resulting in all his times being erased.
When the 25-year-old was forced to pit for a new wing on lap 13, dropping him to plumb last for a second time, it appeared any hope of even finishing in the top 10 was lost.
But the reigning double champion carved his way through the field, aided by a second safety car period when team-mate Mark Webber and Lotus' Romain Grosjean crashed out, to claim third.
Come the end of a pulsating 55 laps around the Yas Marina circuit, Vettel finished just four seconds behind Lotus' Kimi Raikkonen, the Finn winning his first race for almost three years, and three behind title rival Fernando Alonso.
Horner has been amazed by many of Vettel's feats over the years but under a Middle-Eastern twilight, even he was left shaking his head in amazement at this latest achievement.
"We know how consistent Fernando has been this year, so it was entirely predictable that starting from sixth on the grid he was going to be on the podium," said Horner.
"I mentally had an image of him taking 15 or 25 points out of us, so for Sebastian to limit the damage to only three and finish behind him shows what a great drive it was.
"Anybody who doubted he is a racer, he has showed world class. It was one of the best drives of his career. He really went for it, and to go from the pitlane to the podium is phenomenal.
"That's more than I had dreamed of. I thought if we could sneak into the top 10, with it not being easy to overtake here, maybe we could get eighth or ninth.
"But he just drove a phenomenal race."
Horner has revealed how Vettel was unfazed by the stewards' decision post-qualifying, and how that spilled over ahead of the race.
"He was the one guy in the briefing last night saying 'It's not an issue, we can still do this'," added Horner.
"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, and he said 'I'll see you on the podium'.
"He was absolutely convinced going into the race he could get a great result, but then mentally he is incredibly strong.
"It's that mental strength he has that is one of his biggest assets, his key strengths. We've seen it time and time again with him.
"As he continues to evolve and grow, he continues to improve."