The four-time world champion lagged behind Red Bull team-mate Daniel Ricciardo in sixth for most of the final part of the session, but found time on his final run to vault to third and outqualify Ricciardo for only the second time this season.
"The start of that last lap wasn't great, I didn't manage to get the first sector right, [but] I tried to take more risks and it worked, sector two was quicker, I found a significantly better line and kept it together until the end," Vettel said.
"All in all a very good result, the best we could do.
"It was very close - half a second to the Mercedes in front - but four cars within four or five hundredths of a second [behind], so happy to be one of those."
The German is still finding it tough to get comfortable with the RB10, after dominating F1 under the previous rules cycle, but reckoned a cleaner run through practice helped him to his best qualifying result since March's Malaysian GP.
"If you look at the record so far I didn't have the smoothest of races, so it was good to have a clean Friday and Saturday," Vettel added.
"Fingers crossed we have a clean race tomorrow.
"In terms of fighting with the car it is still not where we want to be.
"It is not like last year I was stepping into dream car and everything was smooth and perfect, I had to work hard as well.
"This year we are not yet ticking the right boxes properly."
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