The pair head into the season-ending race at the Yas Marina Circuit locked on points at the top of the championship – only the second time that has happened in Formula One history and the first time since 1974.
Hamilton looked primed to take the advantage as he set the pace for the majority of the sessions heading into the top-10 qualifying shoot-out.
Verstappen, however, put in a scintillating time to seal a 13th pole of his career, with Hamilton coming in second as the title protagonists locked out the front row of the grid.
The track here has undergone changes to promote better overtaking opportunities, but only one winner has come from further back than second on the grid since the first race in Abu Dhabi in 2009.
Hamilton was ultimately pleased to qualify second after conceding his Mercedes could not match the one minute 22.109 seconds which saw Verstappen seal pole – the Brit also joking he was pleased to know where his rival would be given the suggestions he could be run off the track.
“Max did a great lap today so we just couldn’t compete with that time at the end. It was looking really strong in practice,” he said.
“We couldn’t answer that lap, it was a fantastic lap from him, but we are in a good position.
“I couldn’t beat that time he did today and he fully deserved the pole. I’m grateful I can see where he is.
“The car was good, Max did a great job on that final lap. Generally, through practice and into qualifying, the car felt solid.
“The last two laps weren’t easy…I definitely can’t complain, but of course we wish we were a bit quicker today.”
Verstappen did not have it all his own way, however, as he flat-spotted what would have been his race tyre having run wide during the second qualifying session.
The Red Bull will now start on the soft tyre, seemingly not the best race compound, with Hamilton set to start on the preferred medium rubber.
Team boss Christian Horner admitted the flat spot had “forced the hand” of Red Bull on race strategy.
“It is an amazing feeling,” said Verstappen.
“We definitely improved the car again in qualifying. So far this weekend it has been on and off, but I’m incredibly happy with this. It is never easy, especially with their form in the past few races.
“I felt good on both tyres. Naturally in the evening it is a bit cooler, so it should be easier for the soft tyres, but we will see tomorrow.
“Of course in Q2 I had my flat spot on the mediums and had to go out on the softs again. The car felt pretty decent in these final two laps.”
Verstappen also revealed a pre-qualifying plan with team-mate Sergio Perez worked to perfection, the second Red Bull giving a tow in his slipstream to boost the Dutchman’s time on his fastest effort.
“It was discussed before qualifying,” he added.
“It was nicely executed as well, but it is not whatever the gap was. I might have gained a tenth (of a second) towards turn nine.
“Checo is a great team-mate and a real pleasure to work with, also a big ‘thank you’ to him.”
Hamilton, meanwhile, gave a churlish response when asked if a similar tactic had been mooted with his team-mate Valtteri Bottas.
“No, it wasn’t discussed. We have never really done that,” he said.
“I would like Valtteri to focus on him. We work as team, it is never something we discuss or work on and I don’t believe it should be done.”
Hamilton was jeered by a large Dutch support as he spoke after taking second – but claimed that will only spur him on: “There’s a lot of orange here, but I don’t care, it doesn’t make any difference to me.
“It makes no difference to how I go about my life. If anything I use it as fuel, so I am grateful for it one way or another.”
Lando Norris impressed as he took third for McLaren, while the Red Bull of Perez was fourth and the Ferrari of Carlos Sainz fifth ahead of a disappointing sixth for Bottas.
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