Vettel, who is in need of a win in the final two races of the season after a disappointing second half of the year has seen his title challenge implode, was on provisional pole after the first runs in final qualifying.
Vettel had also been quickest in the second part of qualifying, while Ferrari team-mate Kimi Raikkonen set the pace in the first session.
But he failed to improve on his final lap and Bottas was able to sneak ahead by 0.038 seconds.
“It was a nice lap,” Bottas said. “It was so close with Sebastian. Got a clean lap in the end. Lewis was out and I am happy I was able to stand up for us as a team.”
Vettel said: “For tomorrow I think its fine. I think I chickened out a bit on the brakes into Turn One on the final run. The lap was fine. I had time to find on the brakes into the final corner, which I got, but by then I was too far behind.
“But our long run looked good compared to Valtteri so I am feeling good for tomorrow.”
