Ferrari's Fernando Alonso was fourth quickest, but the Spaniard had to abort his fastest lap after running wide.
Lewis Hamilton was fifth fastest for McLaren with Rubens Barrichello an encouraging sixth for Williams.
Despite being over a second slower than Vettel, Hamilton insisted the gap in performance was not as large as it might appear.
"I think we are reasonably close," said the Briton. "We are competitive and I think there is more time to find, so we'll keep pushing.
"We have a good package and they [Red Bull] are probably doing different things to us and we don't know what fuel level they're on. I hope we can at least challenge for the front row tomorrow."
Button was less optimistic.
"I don't know where our pace is but at the moment the Red Bull looks crazy quick," he said.
"It's a Friday though, and so you never really know how quick [they are]. It's unusual for them to show their hand so early."
Alonso said Ferrari would be able to 'fight Red Bull' during both qualifying and the race, while Vettel himself suggested rain could be a factor.
"It doesn't mean so much to be 'P1' today, but it's still good to be on top and we have good pace. The weather may bring a surprise though," he warned.
After the damp and changeable conditions of first practice, the session began with the track largely dry - though there were still damp patches off the racing line - and the teams focussed on making up for lost time.
Hamilton, who only completed nine timed laps during first practice, was quickly out with a one minute 51.7 seconds lap, almost three seconds faster than Webber's first practice time-sheet topper.
The McLaren driver was almost immediately trumped by team-mate Button, who became the first driver to dip under 1.50, and he was soon joined by Alonso.
Ferrari's initial test programme saw the Spaniard running an 'F-duct' while team-mate Felipe Massa ran without, and Alonso laid down a marker by recording consecutive fastest laps.
Jaime Alguersuari had a fortunate escape when his Toro Rosso emerged unscathed after the left rear tyre made contact with the barriers, but there were no such problems for the Red Bull drivers.
After Vettel had gone fastest with a 1.47.824, Webber relegated Alonso to third with a 1.48.584. Button was in fourth, the best part of a second slower than Vettel.
While Adrian Sutil broke the front left suspension on his Force India by bouncing the car over the high kerbs around the chicane, Hamilton and then Alonso split Vettel and Webber.
Button, driving in a more aggressive and hence slightly ragged style than usual, switched to super-soft tyres and went fastest with 1.47.690, but ominously, Alonso was still on the harder prime rubber when he produced 1.47.718.
Vettel followed Button in switching to the option tyres and became the first driver to dip under 1.47, while Hamilton, also now on soft rubber, was over a second slower.
As Vettel continued to raise the bar, Webber moved up to second, but was still almost a second slower.
Alonso, however, had yet to run on the option tyre, and when he finally did so he was faster than Vettel through the first sector of the lap and did a personal best in the middle sector.
But he then ran wide at Turn 17 and down the escape road at Turn 18, and an attempt to recover by reversing back out on to the circuit ended in an ignominious stall.
Marshals pushed the Ferrari back down the escape road, ending Alonso's session, while Red Bull and McLaren settled into race-preparatory long runs on heavy fuel loads.
Robert Kubica, tipped by some for a possible podium finish in Singapore, had his running time severely limited by a hydraulics problem. When the Pole did finally emerge an untidy end to his best lap left him only ninth fastest.
