Second win in a row.
Hamilton further shortens the gap in the bitter world championship fight.
The premiere in Qatar will be the British solo show with a special touch in the fight for human rights.
Verstappen finished second - from seventh on the grid.
Doha - Under the roar of the fireworks over the brightly lit Losail International Circuit, Lewis Hamilton briefly showed the winning fist before he climbed the Formula 1 premiere podium in the controversial Emirate of Qatar in a sweat.
With his new demonstrative rainbow helmet, the seven-time world champion continued his race to catch up in the bitter world championship fight and delivered another demonstration of power on Sunday.
"I drove alone in front, you can enjoy something like that," said Hamilton, who relegated his World Cup opponent Max Verstappen in the Red Bull by more than eight seconds to second place.
"We needed the points today," emphasized Hamilton, before there was alcohol-free rose water instead of sparkling wine.
Verstappen is eight points ahead of Hamilton
After the second success in a row, the 36-year-old Briton is only eight points behind Verstappen with two races to go. The twelve-year-old Dutchman managed to limit damage to the maximum possible after a starting penalty in front of FIFA boss Gianni Infantino's eyes at the Qatar Grand Prix exactly one year before the start of the World Cup. "At the end of the day it was good," he said and was also pleased with the extra point for the fastest race lap before the next controversial race in two weeks in Saudi Arabia and the grand finale in Abu Dhabi.
It is quite possible that only then will the World Cup decision be made.
This was most recently the case in 2016 when Hamilton lost to Nico Rosberg in Abu Dhabi.
"It was certainly not our best weekend because we lacked the speed," said Verstappen, who remained positive: "But there are still two races left, a lot can still happen."
Third place in the 102nd Grand Prix victory after the 102nd Grand Prix pole in Hamilton sensationally went to the two-time world champion Fernando Alonso at the age of 40 in the Alpine.
“I've waited so long for this,” said the Spaniard after shouting “Olé, Olé” in the car - in 2014 he was last on the podium.
Sebastian Vettel scored one point in an Aston Martin in tenth place.
Mick Schumacher was 16 at the Haas.
Verstappen got the best out of a Hamilton who had regained his strength in time for the decisive World Cup phase, after the mood at the former industry leader had already been mighty in the basement.
First Sergio Perez missed the top ten in the qualification in the second car and was missing as a tactical assistant in the fight against the Silver Arrows in fourth place.
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Mercedes driver Lewis Hamilton made the world championship fight with Max Verstappen more exciting again with his victory in Qatar.
© Darko Bandic / AP / dpa
And then, almost two hours before the start of the race, Verstappen also received a five-position penalty for disregarding - albeit incorrectly - double-waved yellow flags in the knockout stages.
Starting position seven instead of two right next to Pole Hamilton.
"It couldn't have been worse," raged Red Bull team boss Christian Horner.
"It's incredible.
We have a billion-dollar sport ”and the International Automobile Federation Fia has no control over the stewards.
One of the marshals had waved twice independently.
Verstappen should have noticed that anyway.
And after his verbal attack on the Fia on Sunday evening, Horner had to go to the race stewards for a report.
World championship fight with hard bandages
Roar and rumble have been part of the poisoned title fight between challenger Red Bull and defending champion Mercedes for weeks.
Silver Arrow team boss Toto Wolff had already declared the end of diplomacy a week earlier when an extremely debatable Verstappen maneuver against Hamilton in Brazil was not even watched.
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So it was not Verstappen but Pierre Gasly who was on the Red Bull (Alpha Tauri) sister team next to Hamilton.
Behind Alonso and Lando Norris in the McLaren, because Bottas also had to go back, but only three places because of the disregard for simply waved yellow flags.
And all three behind Hamilton had the faster, softer tires on it.
Maximum risk of overtaking at the start.
But Hamilton confidently maintained his pole, while Alonso pushed past Gasly and fought hard against rocket starter Verstappen.
The Dutchman rushed past Bottas, who initially fell back to eleventh place, and continued to push, he grabbed Gasly and then Alonso.
After that, little happened at first.
How striking the dominance of Hamilton was a week after his famous victory in Sao Paulo was shown by the time table: Before the first pit stop, Alonso was in third place more than half a minute behind.
And so the superstar, who wants to support the LGBTQIA + community on the Arabian Peninsula with his new helmet design, was able to react relaxed to Verstappen's tire change.
Then he drove deliberately to triumph.
dpa