Mercedes had started at the front of the grid in each of the last 23 grands prix, dating back to the middle of last year, and needed just one more to equal the all-time record, set by the Williams team in the early 1990s.
But the Silver Arrows pairing of Lewis Hamilton and Nico Rosberg were unable to keep pace with the Ferrari and Red Bull teams, who staged their own high-speed battle for pole.
Vettel came out on top, giving Ferrari their first pole position since 2012 with a masterful lap around the floodlit Singaporean track.
The German, a three-time winner in Singapore when he was with his previous team Red Bull, continued his love affair with the tricky street circuit by setting the fastest qualifying time of one minute 43.885 seconds.
Vettel’s pole position was the 46th of his career. His last was in 2013, when he was with Red Bull.
The 28-year-old was more than half a second clear of Australia’s Daniel Ricciardo, who booked his spot on the front row for Red Bull with the second best time.
Finland’s Kimi Raikkonen was third quickest for Ferrari and Russia’s Daniil Kvyat fourth for Red Bull.
Hamilton, who had started from pole in 11 of the previous 12 races this season, could only manage fifth spot, with Rosberg starting alongside him in sixth.
“Our problem this weekend is tyres, they are not giving us a lot of grip and we slide around a lot,” Hamilton said.
“We try to understand why our tyres are bad. We have the quickest car but cannot utilise it with the tyres.”
Dripping with sweat on a hot and humid night in the Southeast Asian state, Vettel climbed from his cockpit and celebrated like he had won the race.
“I know it’s only Saturday and the main job is coming tomorrow but I had to enjoy the moment when I heard that we’d made it,” Vettel said.
“It was looking pretty good, right from the off — and from this morning. The car was fantastic to drive, it got better through qualifying and I think we did the maximum today.
“I’m surprised by the margin but I think it just came together. I really had a near-perfect lap at the end.”
Mercedes have been virtually unbeatable for the past two seasons but the advantage they have with their superior engines is largely negated on slower, tighter circuits such as Singapore, which has 23 turns.
Held at night against the backdrop of the city’s skyscrapers, Singapore provides one of motor racing’s great spectacles on and off the track and is a test of skill and patience for the drivers.
With sparks flying off the back of his car, Vettel dominated the hour-long qualifying session.
He was third after the first stage using soft tyres but accelerated to the top in the second and third phases after switching to super softs.
Ricciardo, who won three races last year when he and Vettel were team mates but has managed just one podium finish this season, made one last, futile attempt to grab pole when he went out on a second set of super-soft tyres but was happy to end with second.
“It’s nice to be back up here. And the front-row as well, it’s been a while,” he said.
“It’s a bit of a coincidence, Seb and I, and hopefully we can have a good race tomorrow.
“It’s a surprise to not see a Mercedes up here. I thought they were playing a few card games yesterday, but they seem to be struggling here.”
(Reporting by Julian Linden; editing by Toby Davis)