The world champion's Red Bull will share the front row with Rosberg's Mercedes, which did two laps good enough for pole.
Vettel was ultimately 0.2 seconds slower than his countryman, but said he was satisfied.
"I'm definitely not disappointed," said Vettel. "Congratulations to Nico, he did a very strong lap. It was all his today.
"When I crossed the line I saw I didn't go first, saw second place on the screen and did not know how much was missing because my lap was fine.
"When I got told the gap to P1 and Nico, it was clear that even with a perfect lap I couldn't have done it.
"Nevertheless I am very happy we managed to save some tyres throughout qualifying.
"It will be all about tyres and tyre deg tomorrow once again. We will see what happens but it's good to start from front row."