Ricciardo dominated the opening day of practice and Verstappen dislodged him at the top of the timesheets on Saturday.
Verstappen, having topped practice three, was the fastest in the first two sessions of qualifying.
Daniel Ricciardo and Red Bull Racing have emerged as the force to beat at the Singapore Grand Prix while pre-weekend favourite Ferrari struggled for pace. "It's a tough race, we'll all feel the pain, but I want this one - I really want it - so hopefully that hunger prevails".
"I'm a little envious today but I'm confident we'll get a victory tomorrow", said the Australian.
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Vettel's impressive streak at the night race includes three straight wins from 2011-13 during his run of four straight F1 titles with former team Red Bull. I squeezed every bit out of it and was just hoping. I think we've got a good package.
Before taking to the Marina Bay Street Circuit at yesterday's practice sessions, Hamilton acknowledged that the bends and twists on the 23-turn circuit favour Red Bull and Ferrari, and the 32-year-old Briton was proven right - at least on one count - that the Red Bulls will take some catching in Singapore.
The tight-turning Marina bay circuit rewards driver bravery over horsepower and Ricciardo has been sweating it out in preparation for the race, which can see temperatures inside the auto soar to 55 degrees and drivers lose three kilograms of fluid in sweat. As the night progressed and temperatures dropped, the scarlet squad had their ground work laid out in terms of tyres, and it became easier to chase the the Red Bull cars.
"Unbelievable. I'm still full of adrenalin", he said.
"We have to believe after today - we'll go for it".
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The pair won four consecutive drivers' and constructors' titles together at the turn of the decade but the relationship has been fractious since a new 1.6 litre V6 turbo hybrid power unit was introduced in 2014.
"I gave it everything today but I could not get any more out of the auto, I squeezed it until it was dry", added Hamilton.
Behind, Jolyon Palmer finished Q2 in P11 in his Renault, missing out by 0.281secs.
The drivers eliminated in first session were Kevin Magnussen, Massa, Stroll, Pascal Wehrlein and Marcus Ericsson.
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