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Red Bull's Verstappen overtook Mercedes's seven-times Formula One world champion Lewis Hamilton in controversial circumstances on the last lap to win the Abu Dhabi Grand Prix and take his first crown.
Mercedes, who still won the constructors' crown for a record eighth year in a row, then protested against alleged breaches of the sporting regulations when the safety car was deployed late in the race.
One was "against the classification established at the end of the competition" and the other argued that Verstappen had overtaken Hamilton while the safety car was still deployed.
Both were dismissed but a Mercedes spokesman said the team had lodged an intention to appeal.
Verstappen had back markers between him and Hamilton after pitting with the safety car deployed and time running out for racing to resume.
In an unusual move, race director Michael Masi first decided lapped cars could not unlap themselves and then changed his mind so that the five cars between the title rivals could get out of the way.
That gave Verstappen a clear run on Hamilton in what amounted to a last-lap sprint finish, with the Dutch driver on fresher tyres.
Stewards found Verstappen had briefly gone in front of Hamilton when both cars were accelerating and braking but was not in front when the safety car period ended.
Mercedes, accompanied by a team lawyer to a meeting with stewards, argued that Hamilton would have won had the rules on lapped cars been complied with and asked for the result to be changed to the positions after the penultimate lap.
The stewards ruled that it was not appropriate to shorten the race retrospectively.
They recognised that while the rules might not have been applied fully, another article allowed the race director to control the use of the safety car.
Win 'insane' - Verstappen
"It's insane," said Verstappen of a race that started with fans on the edge of their seats and ended in uproar, with lawyers looming.
Verstappen's hopes had soared when he qualified on pole position, sunk when he lost the lead at the start and rose again as the safety car came out and race director Michael Masi decisively pushed the boundaries late in the race.
"This is unbelievable guys! Can we do this for another 10-15 years together?" he had said over the radio after the most emotional lap of his life.
"We needed a bit of luck and we got it," said team boss Christian Horner, who had said earlier in the race that it would take a miracle to win and hailed the victory as Red Bull's greatest achievement.
The floodlit race at Yas Marina avoided the collision many had feared, with Verstappen sure to be champion if Hamilton failed to score, but instead left arguments raging long after the finish.
As Verstappen and Red Bull bosses shed tears of joy, Mercedes's management turned on race director Masi.
"Michael, this isn't right," Mercedes principal Toto Wolff had said over the radio to Masi after the Australian's handling of the ending of the safety car period left some feeling Hamilton was robbed.
The safety car had been deployed after Canadian Nicholas Latifi crashed his Williams with five laps to go and Masi then decided not to demand all lapped cars pass it before resuming racing.
That allowed Verstappen -- on fresher, faster tyres after strategic stops -- to close and go wheel-to-wheel with Hamilton for the lead.
Just when it seemed the race would be finishing behind the safety car, which would have handed Hamilton the title, it turned into a sprint finish.
"We were screaming at the end to let them race," said Horner, whose partners Honda are now departing the sport. "It is unheard of to leave the cars unlapped. They wanted to get the race going again. They absolutely made the right call."
Hamilton, who had been heading for a fourth successive race win, congratulated the new champion.
"I think we did an amazing job this year, with my team. Everyone back at the factory, all the men and women we have, and here, worked so hard this whole year," he said.
"It's been the most difficult of seasons and I'm so proud of them, so grateful to be a part of the journey with them. We gave it everything this last part of the season and never gave up, that's the most important thing."
Verstappen ended the season with 10 wins to Hamilton's eight, having also led more laps and taken more poles and podiums.
After 22 races, Verstappen had 395.5 points to Hamilton's 387.5. Mercedes scored 613.5 to Red Bull's 585.5.
Ferrari's Carlos Sainz finished the race in third place, with AlphaTauri's Yuki Tsunoda fourth and team mate Pierre Gasly fifth.
Hamilton's team mate Valtteri Bottas was sixth in his last race for the team, ahead of McLaren's Lando Norris and the Alpines of Esteban Ocon and Fernando Alonso.
Ferrari's Charles Leclerc took the final point with the Italian team ending the season third overall.
Verstappen's Mexican team mate Sergio Perez, hailed as a "legend" by the Dutch driver for slowing Hamilton significantly while leading earlier in the race, was retired in the pits.
The race hit immediate controversy on the opening lap when the title rivals almost collided after the Briton had taken the lead.
Hamilton was pushed wide, cutting a corner as he came back still in front of Verstappen who had made a lunge on the inside and seemed to be ahead at the turn, and stewards decided no investigation was needed.
Horner told Sky Sports television from the pitwall that there was "a total lack of consistency" in the stewards' decision and his team now had to "do it the hard way".