|Singapore Grand Prix on the BBC|
|Venue: Marina Bay Circuit Date:18-20 September|
|Coverage:Highlights on BBC TV at 17:10 BST, video highlights on the Sport website|
Vettel put in a sensational performance to qualify fastest by 0.543 seconds from Red Bull's Daniel Ricciardo as Ferrari claimed their first pole since the 2012 German Grand Prix.
Ferrari's Kimi Raikkonen was third ahead of Red Bull's Daniil Kvyat. Hamilton's team-mate Nico Rosberg finished sixth.
Williams's Valtteri Bottas was seventh, split from team-mate Felipe Massa in ninth by Toro Rosso's Max Verstappen, as Lotus's Romain Grosjean completed the top 10.
How did Ferrari do it?
Ferrari do have improvements to their car - they are using an upgraded engine that made its debut at the last race in Italy and have some aerodynamic revisions.
Vettel did not even need to complete his final flying lap as his first time in the top 10 shoot-out was still good enough for pole by more than 0.1secs when all his rivals had finished their last laps.
But he carried on anyway and whooped with delight after crossing the line to become the first Ferrari driver on pole since Alonso at Hockenheim in July 2012.
It was also Ferrari's first pole in the dry since Singapore five years ago - when Alonso converted it into a narrow victory from Vettel, who was then at Red Bull.
And Red Bull were always expected to go well at Marina Bay this year, a track that emphasises their chassis strengths and masks the deficiencies of their Renault engine.
But it seems Mercedes have fallen back as much as their rivals have caught them up - Hamilton was 0.3secs ahead of Bottas, a much smaller margin than would have been expected.
Hamilton said Mercedes are having trouble generating tyre temperature.
He will be relieved his 53-point championship lead means he has no real need to be concerned and can focus on damage limitation in Sunday's race - live on the BBC Sport website at 13:00 BST, 5 live and highlights on BBC One at 17:00 BST.
Hamilton: 'We have the quickest car'
Hamilton said: "I enjoyed qualifying. The laps weren't perfect. I was on the knife edge trying to close the gap. The problem this weekend is the tyres are just not working for us. We can't get it into the window and we are sliding around all over the place.
"We have been trying to understand. We do have the quickest car but for some reason the tyres were not switching on and it is apparent on both cars. We have never seen it before."
Vettel said: "It was looking pretty good from this morning and the car was fantastic to drive. It just got better through qualifying. I am surprised by the margin but it all came together and I nearly had a perfect lap in the end. I was very, very happy with the laps, especially the last one."
Ricciardo added: "Front row; it's been a while. It should be a good race."
McLaren make progress
McLaren did not achieve their hope of getting a car into the final part of qualifying, but Fernando Alonso still produced their best showing for some races.
The Spaniard was 12th fastest, three places and 0.691secs ahead of team-mate Jenson Button.
From there, Alonso will be optimistic of achieving his aim of a solid points finish in the race.