Hamilton claimed the lead of the 2017 World Championship from Vettel for the first time a fortnight ago at Monza, a race in which Mercedes routed Ferrari on the Italian team's home ground.
Championship rival Lewis Hamilton, who leads Vettel by three points in the standings, could only qualify fifth as the Mercedes struggled in high downforce conditions.
"I still believe we can win - I'm still confident we'll get victory", said Ricciardo, who has finished on the podium in the last three straight races in Singapore and came within half a second of victory previous year.
We knew coming here it would be hard. "We had a hard night yesterday but a better night today and I'm sure the auto will be like today tomorrow, so it will be better but for sure it will be a close race". "It's important that we obviously keep that but I have a lot of faith we can stay there all weekend", he said.
"I got everything I could out of the vehicle, everything and more", he added.
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"The drivers extracted everything there was from the auto - we've been quickest in every single session this weekend, and then the one that really counts. we just don't have that last little bit", he reflected. "I threw the sink at it and squeezed every bit of it".
Hamilton was also surprised at Vettel's pace but he warned that Sunday's notoriously long, hot and physical race was "a marathon not a sprint". "But if not then you just settle down and get into the race".
"The oil seems everywhere in the final sector", complained Toro Rosso's Daniil Kvyat, as the early times were far slower than those seen in practice.
Hamilton felt happy he had maximised his own effort - which left him less than 0.1s shy of Kimi Raikkonen - but admitted Mercedes had doubted Ferrari had the pace to snatch pole.
Daniel Ricciardo put on a dazzling display under the floodlights as Red Bull laid down a marker on the opening day of Singapore Grand Prix practice on Friday.
Vettel is a four times victor in Singapore and the pole was also his fourth in the city state.