Less than two seconds covered the top four at the chequered flag as Hamilton ignored instructions from the Mercedes pit wall to up his pace in the closing laps. Daniel Ricciardo followed his Red Bull team mate home, with Ferrari's Kimi Raikkonen taking sixth ahead of Force India’s Nico Hulkenberg and Sergio Perez. Williams’ Felipe Massa and McLaren’s Fernando Alonso completed the top ten.
The start saw the two Mercedes lead off the line, with Hamilton heading Rosberg, as Raikkonen passed Ricciardo for third. Things got worse for Red Bull as Verstappen, in sixth, ran out of room exiting Turn 1 and spun after making light contact with Hulkenberg.
That forced the team to switch the Dutchman to a one-stop strategy as he fell to last place, and would have its effect later on.
Hamilton and Rosberg moved clear until their first pit stops, respectively on the seventh and eighth laps, after which Hamilton led again but with Verstappen having risen to second ahead of Rosberg.
The German was then content to follow him for the next 12 laps before finally slicing by the Red Bull, with a closely-fought but crucial pass. After that he got the throttle down, cutting a 5.8s gap to Hamilton to 3.1s by the time they stopped again, on laps 28 and 29.
That was when Hamilton was forced to try to back up his team mate, as he needed him to finish fourth or worse, and the gap came down to less than a second thereafter as the outgoing champion did all he could to let Ferrari and Red Bull catch up.
When Ferrari kept Vettel out until lap 37 before switching him to supersoft tyres, when everyone else was running softs, the German suddenly became the dangerman.
He passed team mate Raikkonen for fifth on the 41st lap, then set out after Ricciardo, who was having a subdued run in fourth. He passed the Red Bull on lap 47, and that set up the final showdown.
On his worn softs - he had pitted on lap 21 - Verstappen just wasn’t able to get closer than within three seconds of Rosberg as Hamilton continued to lap at a relatively slow pace despite being implored - and at times directly told - to speed up by his Mercedes bosses.
Vettel eventually out-dragged Verstappen’s Red Bull on the 51st lap, and Hamilton, Rosberg and he then circulated nose to tail. They were having kittens at Mercedes, especially as Hamilton told them quite trenchantly that if he was losing the world championship he didn’t particularly care if he lost the race as well.
In the end, of course, he was never going to do that. He did everything that he could, and crossed the finish line 0.4s ahead after 55 laps to score his 10th win of the season, the 53rd of his career - and to lose his world title.
Rosberg kept his cool despite the pressure from Vettel, but said it had been tough.
“That definitely wasn’t the most enjoyable race I’ve ever had!” he admitted. “With Max early on, and then with these guys coming at the end, it definitely wasn’t fun. I’m just really glad it’s over!”
For Vettel, third was a decent way to finish the season, with Verstappen taking fourth from his team mate and the distant Raikkonen.
Hulkenberg took a fine seventh for Force India, and with team mate Sergio Perez eighth Force India easily secured their fourth position in the constructors’ stakes. But Perez only just got home ahead of the fighting Williams of Felipe Massa, who signed off on his F1 career by maintaining his record of scoring points in each Abu Dhabi Grand Prix in which he has competed, and Fernando Alonso, who took the final point for McLaren.
Alonso’s team mate Jenson Button was in contention for points in his final Grand Prix, until a right-front suspension failure put him out after a heavy kerb contact. He was joined in retirement by the Toro Rossos of Daniil Kvyat and Carlos Sainz, Williams’ Valtteri Bottas and Renault’s Kevin Magnussen.
Outside of the points, Romain Grosjean led outgoing Haas team mate Esteban Gutierrez home in 11th and 12th after a race-long fight, as an equally intense intra-team fight between Esteban Ocon and Pascal Wehrlein ended in the Frenchman’s favour after they had a brief collision. Likewise, Marcus Ericsson narrowly led home Sauber partner Felipe Nasr in 15th and 16th, as Jolyon Palmer was the final finisher, penalised five seconds after a collision with Sainz.
Afterwards, Hamilton shook hands with the man who has taken his crown, and they hugged on the podium.
“Winning the championships is a great feeling, Hamilton said as he congratulated his team mate, “and I’m looking forward to fighting with him for it again next year.”
Rosberg, meanwhile, looked forward to celebrating with his father Keke and mother Sina, and did so in the moment with his wife Vivian, on the greatest day of his racing career. It would, he admitted, take some time before it really sank in.