After all the suspense and expectation, Hamilton chalked up his 10th win of the season, and fourth in a row, but was powerless to do anything about the championship outcome despite making every effort.
His attempt to push Rosberg into the clutches of those behind him, by deliberately slowing the pace in the closing laps to the concern of team bosses, produced a nail-biting finish with the top four separated by just 1.6 seconds.
“Lewis, this is Paddy we need you to pick up the pace to win this race,” the team’s technical head Paddy Lowe told the Briton over the team radio.
“Right now, I’m losing the world championship so I’m not bothered if I’m going to lose the race,” replied Hamilton, who crossed the line 0.4 seconds ahead of Rosberg with Ferrari’s Sebastian Vettel third and a further 0.4 behind.
The frosty atmosphere between the pair as they waited for the podium ceremony spoke volumes, with Rosberg hoisting the sport’s 86-year-old commercial supremo Bernie Ecclestone into the air but ignoring Hamilton.
There was minimal eye contact between them, let alone a handshake.
The hug, the handshakes and a word of congratulation, eventually came on the podium.
“That was definitely not the most enjoyable race I’ve ever had… really not very enjoyable those last laps,” said Rosberg in podium interviews conducted by former F1 racer David Coulthard.
“I’m glad it’s over, and I am ecstatic.
“It was really intense and tough out there.”
Rosberg, who had needed only to finish in the top three to be sure of the title, settled into second at the start as Hamilton streaked clear but the Briton’s strategy was immediately apparent.
He made little effort to build up a commanding lead, knowing that his only hope of becoming Britain’s first four-times champion depended on denying Rosberg clear air and allowing rivals to get close enough to pass.
“It was tricky at the end there with Lewis playing some dirty tricks,” commented four-times champion Vettel over the radio.
Rosberg, who becomes his country’s third champion after Michael Schumacher and Vettel, held his nerve and position just as he has throughout a season in which he has insisted on taking one race at a time.
As he crossed the line, the son of 1982 title-winner Keke Rosberg let out a whoop of relief and joy as he became only the second son of a world champion, after Britain’s Damon Hill, to take the crown.
In another emotional touch, the tearful 31-year-old’s wife Vivian spoke to him over the team radio on his slowing down lap to tell him how proud she was. His own pride was equally evident.
“I am very proud to have done the same feat as my dad achieved, he is going to be coming in half an hour I think,” said Rosberg, whose father was not at the circuit and has been present for only his home Monaco Grand Prix this year.
At the same time, Hamilton knew he would have to explain himself to unimpressed team bosses.
“We first have to speak to him to get an explanation,” said non-executive chairman Niki Lauda. “We tried to tell him the danger was coming because Vettel had the fastest car at the end. Thank god it worked out in the end.”
Red Bull’s Max Verstappen finished fourth, another remarkable race for the Dutch teenager who spun at the start and fought back from last place. His Australian team mate Daniel Ricciardo was fifth.