With four times world champion Vettel three cars ahead and favorite for his fourth Singapore success on Sunday, Hamilton will be hoping for damage limitation before returning to more favorable tracks.
"At the end of the day, to be second here, on this track, I think it is very promising", said 19-year-old Verstappen, who could have been the youngest driver in the history of the sport to start on pole.
He then survived a light brush of the wall at the right-hander coming out from under the grandstand on his second run to improve to a 1m39.491s to take pole from Red Bull driver Max Verstappen by 0.323 seconds.
Qualifying would suggest Hamilton is set to lose his slender three-point lead over Vettel in the championship on Sunday.
"The vehicle was tricky but it came alive and it was getting better and better as the night progressed, so I'm really happy that we got it done".
When asked if he could take confidence from Mercedes' long-run pace on Friday, Bottas said: "I have to say I'm not going into tomorrow with great confidence in my pace".
"We know we still have to work hard to improve [in qualifying] - it is still not where Ferrari and Mercedes is".
"I got everything I could out of the vehicle - I got everything and more, I literally threw the sink at it".
DANIEL Ricciardo has led a Red Bull one-two in second practice for the Singapore Grand Prix. "I knew we had it in us, it was a bit of a struggle to get there but now I'm just happy". "There seems to be a certain pattern that some cars go better on the slow, twisty stuff".
The Red Bulls headed out in a bid to respond, with Verstappen reclaiming top spot by just a fraction of a second. "I definitely didn't anticipate Ferrari would be as strong as they were". I gave it everything and more.