McLaren's Australian rookie Oscar Piastri qualified third for McLaren with Mercedes' George Russell fourth.
McLaren's Lando Norris dropped from a provisional second after the first flying laps to an eventual fifth when he clipped a kerb on his final effort.
"The whole weekend so far has been a bit of a struggle so we definitely improved the car for qualifying," said Verstappen, who can end the year with a record-extending 19th win in 22 races.
"From lap one it all seemed a bit more together and we could definitely push more."
Red Bull have won 20 of the 21 races so far, another F1 record, and Verstappen has won in Abu Dhabi for the past three years. Both titles have already been clinched.
The Dutch driver, whose teammate Sergio Perez qualified in ninth place, had complained in practice about his car jumping around 'like a kangaroo'.
Russell had been fastest in two of the practice sessions and Leclerc in the other, raising hopes elsewhere that Verstappen might not have it all his own way and raising doubts even within Red Bull.
"Well done mate. You've just won me 500 euros off (Red Bull motorsport consultant) Helmut (Marko) which is like getting blood out of a stone," a jubilant team boss Christian Horner told Verstappen over the team radio.
"Helmut lost a bet? What world are we living in?," replied Verstappen.
"The bet was for you to be on the front row, mate," said Horner.
The pole was Verstappen's 12th of the season, equalling 1992 champion Nigel Mansell's career haul of 32 - which is seventh equal in the all-time lists.
HAMILTON 11TH
McLaren looked a good bet to retain fourth place overall, with rivals Aston Martin having only Fernando Alonso qualify in the top 10, the Spaniard lining up seventh and behind AlphaTauri's Yuki Tsunoda.
Mercedes' seven-times world champion Lewis Hamilton qualified only 11th, knocked out by Russell.
The 38-year-old Briton had complained to race engineer Peter Bonnington over the radio that "there's something not right with this car".
Ferrari's Carlos Sainz went out at the first hurdle and will start 16th in a blow for the Italian team's hopes of overtaking Mercedes for second overall in the constructors' standings.
The two teams are only four points apart in the main remaining battle of a championship dominated by Red Bull and Verstappen.
Sainz was knocked out in the dying seconds of phase one by Perez, who went from the danger zone to second behind Verstappen, after being last out of the pit lane at the end and then hitting traffic.
"Some of the guys that had finished the lap I don't think they got out of the way very nicely but it's our fault, we went out too late," said Sainz.
"We had a problem with the front wing that delayed us quite a bit so we just need to have a look at what we could have done better."
Aston Martin's Lance Stroll qualified 13th.
Williams' Logan Sargeant will line up last of all after his best lap was deleted for exceeding track limits, the U.S. rookie ending the season having been outqualified by teammate Alex Albon in every race.
Albon will start 14th and with AlphaTauri's Daniel Ricciardo 15th, with the two teams separated by seven points in a battle for seventh overall.
