Ferrari lock out the front row leaving Mercedes to fill the second row.
The new five-time world champion clocked a track record best lap in one minute and 7.281 seconds on his second run in the final session.
Vettel will have to deal with Red Bull's Daniel Ricciardo immediately ahead of him as well as Hamilton's teammate Valtteri Bottas.
Hamilton topped the times with a late flying lap that kept him narrowly ahead of his only remaining title rival Sebastian Vettel.
Lewis Hamilton wins the Japanese Grand Prix while Sebastian Vettel, the Briton's closest rival, finishes sixth.
The four-time champion Briton clocked a best lap time of one minute and 33.385 seconds to outpace the Finn by two-tenths of a second at the Sochi Autodrom circuit where title rival Sebastian Vettel was fifth quickest.
The German arrived in Singapore 30 points behind Hamilton, with only seven races left to overhaul the Mercedes driver.
The chances of Raikkonen being allowed to take victory would seem remote to most observers, given his and the team's track record.
Vettel lapped the Monza circuit near Milan with a best time of one minute 21.105 seconds.
The German four-time champion, who is 24 points behind defending champion Lewis Hamilton in this year's title race, clocked a best lap in 1min 42.661sec.
Vettel acknowledged that he had to overcome some emotional and mental strain in recent days.
The championship leader, racing on home soil for the first time in two years, painted a gloomy picture of the future, however.
The difference between the four times world champions came down to just 0.044 seconds at the end, with Vettel 0.057 faster after their first flying laps around a sizzling Silverstone circuit.
The championship leader accepted, however, that drivers should carry some of the blame for complaining in the past of inconsistencies in stewards' decisions which had led to a more rigid approach.
It is the Italian team's first time on pole in Montreal since seven-time champion Michael Schumacher managed it in 2001.
Sebastian Vettel clocked the fastest time on Saturday in the final practice for the Chinese Grand Prix, as Ferrari upped the pressure on Mercedes and defending champion Lewis Hamilton, who managed only fifth-best.
Sebastian Vettel won the season-opening Australian Grand Prix for Ferrari, ahead of Lewis Hamilton for Mercedes and Ferrari teammate Kimi Raikkonen.
Four-time world champion Sebastian Vettel smashed the lap record at Montmelo in Formula One testing on Thursday when he clocked 1min 17.182 in his Ferrari but dismissed it as insignificant.
Ferrari's Sebastian Vettel delivered the fastest time in Formula One testing on Tuesday as warmer conditions greeted drivers in Barcelona following last week's snow-hit sessions.