Ricciardo dominated the opening day of practice and Verstappen dislodged him at the top of the timesheets on Saturday, with the Dutchman going fastest in the opening two phases of qualifying.
It was also his third of the season but he had to put everything on the line when it really mattered to beat the Red Bulls in a close-run session, lighting up the timing screens with a lap of one minute 39.491 seconds.
"I am happy we got the vehicle where it deserved to be, then we take it from there", Vettel said.
Singapore Grand Prix polesitter Sebastian Vettel was left surprised by his qualifying pace, saying his auto "came alive" in the final session.
Had he been on pole, the 19-year-old would have been the youngest driver in the history of the sport to start from the top slot.
"I knew we had it in us".
The result left Ricciardo slightly disappointed but the Australian remained confident he could win the race on Sunday. "It was a bit of a struggle to get there but now I'm just happy", Vettel said. "I've just got to try and keep the pressure on the guys in front without cooking my auto, if I can".
Bottas says of the deal: "I've been very impressed by the mentality, commitment and the team spirit this team holds".
That in itself could be a tough task, with Ferrari's Kimi Raikkonen also ahead of the Briton and Singapore a notoriously hard circuit for overtaking.
There was a flurry of activity when the session was restarted, with Vettel setting the fastest first and second sectors to go quickest with a 1m41.901s, 0.348s quicker than Verstappen. The auto was tricky but was getting better, better and better.
"Here, what I've seen today, Red Bull is outstanding. For some reason Ferrari are slower, I don't know why".
"I got everything I could out of the vehicle, everything and more", he added.