Nico Rosberg won his first Formula 1 world title despite Lewis Hamilton disobeying Mercedes orders not to back his team-mate into rivals.

Hamilton won the Abu Dhabi GP driving slowly in an attempt to bring other drivers into the battle, knowing he needed Rosberg to finish below third.

Hamilton was repeatedly told to speed up but told the team: "Let us race."

Rosberg came under pressure from Sebastian Vettel but held off the Ferrari driver to finish second.

Relief: Rosberg has been racing in Formula 1 for a decade before taking his first title

Rows over the radio

Hamilton controlled the race from the front but was under instruction from Mercedes management not to try any strategic games to delay Rosberg.

However, he disregarded message after message to speed up and prevent Vettel and Red Bull's Max Verstappen from closing on Rosberg.

The German in turn complained on the radio to the team to "consider doing something" and the tense title battle will do nothing to improve the cool relationship between the two drivers.

At one point, as Vettel homed in on Rosberg in the closing laps, Mercedes executive director (technical) Paddy Lowe, who only speaks to the drivers on the radio in extreme circumstances, told Hamilton: "Lewis, this is Paddy. We need you to pick up the pace to win this race."

Hamilton replied: "I'm in the lead right now. I'm quite comfortable where I am."

But his tactics were not enough and Rosberg whooped with delight as he crossed the line and, after wife Vivian congratulated him over the radio, did doughnut spins on the pit straight before climbing on to the nose of the car to take the cheers from the crowd.

Doughnut, anyone? Rosberg performed 360-degree spins on the start-finish straight

A positive end to an intense battle

"It's a childhood dream come true," Rosberg, 31, said over the radio. "Thank you for everything."

After the drama of the race, Hamilton congratulated Rosberg on his world championship and the two men embraced and shook hands on the podium.

Rosberg said he had not decided whether to take the number one on his car as is his right next year or whether to stick with the number six, which he chose as his race number because his father Keke won the 1982 world title with it.

The Rosbergs are only the second family in which a father and son have won the F1 world title, after Graham and Damon Hill.

Rosberg is the second son of an F1 champion to win the title himself. Here's father Keke winning his back in 1982. Diana Ross did not actually finish on the podium

And 34 years later, Vettel had the honour of celebrating with Rosberg on the podium. Source: Forix

A very tense race

Rosberg started the race 12 points ahead of Hamilton, and knew a podium finish would be enough to secure the championship regardless of what Hamilton did.

It initially looked as though he would be able to cruise to an easy climax to the best season of his career, but it did not take long for the tension to mount.

Hamilton and Rosberg both made good starts to convert first and second places on the grid into a one-two from the start.

But the difficult moments for Rosberg began when he came out from his first pit stop behind Red Bull's Max Verstappen.

After a spin at the first corner of the race, the Red Bull driver recovered ground quickly and, running a long first stint as a prelude to a one-stop race, ended up in second place behind Hamilton after the leaders had finished their first pit stops.

Rosberg came out right behind Verstappen, and was also under pressure from behind from Ferrari's Kimi Raikkonen, Red Bull's Daniel Ricciardo, and Vettel.

Ricciardo attacked Raikkonen intermittently, without managing a pass, but Rosberg was able to stay out of the Ferrari's reach and the Finn never got close enough to try the same to the Mercedes.

Rosberg becomes the 14th driver to win a maiden F1 title as a father. Source: Forix

Rosberg shows he can overtake

Rosberg tried to pass Verstappen two laps after his pit stop but the Dutchman defended aggressively and the championship leader decided discretion was the better part of valour and sat back looking after his tyres.

However, as Verstappen's stint grew longer and longer, Mercedes realised they were at risk of losing second place to him because he could make his one stop for tyres and still come out in front.

Rosberg was told on lap 19 that passing the Red Bull was "critical" and he responded by passing Verstappen on the next lap to take the second place he would hold to the end.

Hamilton continued to lap only just as fast as he needed, balancing his vain hope that other drivers might be able to get among the two Mercedes with instructions from his team not to drive too slowly and force the issue.

That's 12 F1 world drivers' titles now won by Germans

Vettel: 'Lewis playing dirty tricks'

As the race progressed, Hamilton went slower and slower and the team began to worry that a one-two was at risk.

This ensured Verstappen was never more than about three seconds behind, with Ricciardo closing on him and, in the final stint, Vettel attacking both.

With 11 laps to go, Hamilton was warned to pick up the pace because Vettel was an "imminent threat".

At the time, Vettel was running in fifth place but was closing rapidly on Verstappen and Ricciardo in third and fourth places because the four-time champion had done a long middle stint and fitted super-soft tyres for his final stint, while the others were on the more durable but slower soft tyres.

He passed both but was not quite close enough on the last lap to make an attack on Rosberg work.

"It was a tricky situation at the end with Lewis playing dirty tricks," Vettel said to his team as they congratulated him over the radio.

"It was tough out there. I didn't want to be an issue. But at the end I was thinking maybe to try to pass both of them but it didn't work out."

Hamilton denied using dirty tricks to hamper Rosberg.

Nico and his wife Vivian receive the champagne showers treatment

While Hamilton's glum expression told the story of the outcome of the title fight

A sad end for Button

Jenson Button's final grand prix came to an early end when his McLaren's front suspension broke as he bounced over a kerb on lap 12.

Button said: "The result doesn't count. The weekend does. It has been awesome, from the fans, to before the race, a load of the team lined up and I walked between them and they clapped me into the garage. Very emotional, not the easiest thing before a grand prix. An amazing day and an amazing weekend."

Williams driver Felipe Massa, who is also retiring from F1, finished ninth, fending off a late attack from former Ferrari team-mate Fernando Alonso's McLaren.

His long-time friend and engineer Rob Smedley praised him on the radio afterwards, saying he had had a "great drive".

Button said goodbye to Formula 1 after 17 years - three of them spent as team-mate to Hamilton

The sights

The race takes place at dusk in the desert...

...the perfect time of day for Rosberg to celebrate

...and everybody else in attendance...

...Including tennis ace Roger Federer and his wife Mirka

The German showed some love to his championship-winning car

Felipe Massa's son waved goodbye as his dad headed out for his final grand prix appearance. Williams let the Brazilian driver keep his car as a retirement gift

The stats

How Rosberg and Hamilton matched up in 2016

Rosberg may have had the better of the reliability this season, leading some to say he does not deserve his title, but it has not always been that way

Longest wait for an F1 title: Mr Rosberg slots nicely into second here: with a 10-year wait over 206 races. Source: Forix

Abu Dhabi Grand Prix results