The defending three-time champion dominated the session and clocked a fastest time in one minute and 38.755 seconds to beat the championship-leading German by three-tenths of a second.
Hamilton's performance gives him the ideal opportunity to claim a fourth consecutive victory in Sunday's race in which Rosberg can secure his maiden drivers title if he finishes on the podium.
Hamilton, who trails Rosberg by 12 points, said: "I didn't over-cook into turn one and after that I was in total control.
"It's been a great weekend so far.
"I've got the car in a real sweet spot, with some great work done by my engineers and faultless mechanics who've done an incredible job."
"Lewis did an incredible job - a really incredible job - and you can't say more," said Mercedes team non-executive chairman Niki Lauda.
It is the Briton 12th pole of the season, a personal record, his third in Abu Dhabi and the 61st of his career. In the process, he ended Rosberg's hopes of a third consecutive pole at the circuit.
Rosberg reflected: "I came here to take pole and win the race and so I am not ecstatic about today, but Lewis did a great job.
"I felt good out there and had a good balance and got a good lap in the end, but it wasn't good enough."
Australian Daniel Ricciardo produced a scorching late lap to take third for Red Bull ahead of Kimi Raikkonen and his Ferrari team-mate Sebastian Vettel and Dtuch teenager Max Verstappen in the second Red Bull.
Nico Hulkenberg was seventh for Force India ahead of his team-mate Sergio Perez, Fernando Alonso of McLaren and retirement-bound Brazilian Felipe Massa who was 10th for Williams.
As the sun went down in a blaze of distant late heat, retirement-bound 2009 champion Jenson Button was on top after eight minutes to the delight of his mother and sister, grinning in the McLaren garage.
Hamilton and Rosberg joined the fray with the defending champion clocking his lap in 1:39.487 to go top ahead of his Mercedes team-mate by a full second.
By the end of Q1, Hamilton's lap remained quickest ahead of both Ferraris and Verstappen ahead of Rosberg.
Out went Daniil Kvyat in his Toro Rosso together with Kevin Magnussen of Renault, Felipe Nasr of Sauber and Esteban Ocon of Manor.
Surprisingly, Carlos Sainz was also eliminated in 21st place in the second Toro Rosso ahead of Marcus Ericsson of Sauber.
Pascal Wehrlein escaped the 'drop six' and made it into Q2 in the final seconds together with Jolyon Palmer of Renault. "Whooo-hoo, easy-peasy," sang Wehrlein on team radio.
Hamilton was quickly out and back on top in Q2 with an improved lap in 1:39.382.
That was good enough for him to lead the way as Rosberg tried to eliminate a few minor errors and draw level, finishing one-tenth down but ahead of Raikkonen and Verstappen.
In a final flurry of action, Massa and Alonso made it through to the top ten shootout and knocked their respective team-mates Bottas and Button out.
They missed out along with Mexican Esteban Gutierrez and his Haas team-mate Frenchman Romain Grosjean, Palmer and Wehrlein as darkness descended and the track temperature dropped to 29 degrees Celsius.
Hamilton was out swiftly again to improve with an initial lap in 1:39.013 ahead of Rosberg, who pushed hard, but was still down by three-tenths of a second again in second place.
It set up a dramatic finale with Hamilton out first again to prove his mastery again with a smooth and supreme performance.