Vettel's final lap of 1:37.642 was the quickest of the session, half a second clear of Hamilton in second.
The German, winner of the past two Grands Prix in Singapore and Japan, has never started off the front row at Korea.
He gave himself the perfect chance to extend that run with a fantastic late run on the super softs, improving his own personal best several times and working his way down to a 1m37.642s.
That put him comfortably clear of the chasing pack, which was led by McLaren's Hamilton.
The Briton had been more of a match for Vettel on the softs, but was unable to match the German's improvements in the final minutes and on the red super soft compounds.
Button finished third in the second McLaren, while Lotus's Romain Grosjean and Kimi Raikkonen - the latter running with the Coanda-effect exhausts - secured fourth and fifth.
Championship leader Fernando Alonso was sixth fastest ahead of Mark Webber, who was prevented from completing a super soft run by electrical engine issues.
Ferrari's Felipe Massa, Williams's Pastor Maldonado and Force India's Nico Hulkenberg rounded out the top 10. Hulkenberg finished 1.2s down on Vettel.
The session began in understated fashion, with a dearth of on-track action once the initial round of installation laps was completed.
That situation was finally remedied 16 minutes in when Daniel Ricciardo and Kimi Raikkonen headed out.
The latter's second flyer, a 1m39.748s, kept him top while Pastor Maldonado, Nico Hulkenberg and Jean-Eric Vergne joined the fray, but he was demoted by Vettel when Red Bull emerged 24 minutes into the running.
Four minutes on Webber confirmed the team's pace by dropping the benchmark to a 1m38.766s, which would keep him top until the final 20 minutes.
At that stage Ferrari and McLaren were both yet to go out, but when they did it was with an instant impact.
The Scuderia was the first to bite, and at the session's halfway mark Alonso shot up into second.
Minutes later McLaren also joined the track, with Hamilton and then Button demoting the Spaniard. Hamilton's second effort was enough to finally relegate Webber and put the Briton top.
He was soon joined by Button, who set the fastest time in sector two en route to making it a McLaren 1-2 at the top of the charts.
That didn't last long however, as Vettel shot back to the top with a 1m38.215s, around three tenths of a second faster than Hamilton.
That would be as fast as anyone achieved on the soft compound, with the majority of the field pitting for a switch to super softs shortly after Vettel set his mark.
Aside from Webber's late issue, there were relatively few issues during the 60 minutes.
Bruno Senna was urged to pit for a front wing complaint, although Williams managed to rectify the problem with a minimum of fuss, while Caterham's Vitaly Petrov was warned not to cross pedals late on.
The Russian was still able to edge out team-mate Heikki Kovalainen to finish 19th, just behind Senna.
HRT's Narain Karthikeyan meanwhile felt he had cause for complaint when baulked slightly by Sauber's Sergio Perez, an incident not dissimilar to the one which earned Michael Schumacher a Friday reprimand.