Lewis Hamilton dedicated his fourth Hungarian Grand Prix win and his first victory for Mercedes to ex-girlfriend Nicole Scherzinger and described the victory as a "Band Aid" which would temporarily heal his troubles off the track.

He delivered one to join racing legends such as Juan Manuel Fangio and Stirling Moss as winners for the three-pointed star team, and then admitted his surprise that the race had been so straightforward.

This professional success comes against the backdrop of turbulence in his personal life, following the break-up of his relationship with popstar Scherzinger, and he told several national newspapers: "It has not been the easiest few months.

"It feels a little bit odd without that someone here - but I would say now that this is one of those races you want to dedicate to that someone.

"The thought in my mind through the whole race was of someone really special to me and I want to dedicate it to her. For the next few days, this will keep me riding high. It is a bit of a Band Aid that will cover me for some time."

In spite of starting the race in a surprise pole position, Hamilton had forecast more of the tyre problems that have blighted Mercedes’ season so far, and declared that victory would require a miracle.

Afterwards he said that against his expectations the final 20 laps had been a “walk in the park” as he kept ahead of the battling Kimi Raikkonen and Sebastian Vettel. “This is probably one of the most important grand prix wins of my career, with my new team,” he smiled, the relief of finally getting the monkey off his back all too evident. “Driving for Mercedes is a real privilege and I’m very proud to be part of the team and hope there are more wins to come.”

Hamilton had feared that the new tyres would give the other teams even more of an advantage, especially as Mercedes were banned from testing them last week after an earlier breach of rules.

“I came here praying that when we put Pirelli’s revised tyres on that they would come to us rather than going away further from us, and it seems that they have. We were on our back foot because we were the only ones who weren’t allowed to test them at Silver-stone last week, and I really wasn’t expecting this which is why I talked it down yesterday. But in the end it was a walk in the park, and I’m baffled, to be honest, because all the techniques I used to save the tyres worked today whereas they haven’t always in the past. If we can come here and make our tyres last, we should be able to do it elsewhere.

“To win for Mercedes at last is so important for me. It was exceptional, a really calming, relaxing feeling when I crossed the finish line.”

While Hamilton revelled in his car’s new-found performance, Vettel lost crucial time behind Jenson Button’s McLaren, and the delay was crucial. “Seb was a little bit quicker but he was behind,” Hamilton said. “My tyres went off a little bit quicker than his but I called the pit stop okay. When I came out behind Jenson I thought that was just my [bad] luck, but I passed him and was surprised to see others stuck behind him, so he did me a favour.”

Vettel agreed: “This is not the best circuit to be stuck in traffic as it’s very difficult to overtake. I was stuck behind Jenson for some time and I damaged my front wing, which was my fault. I tried to fight back, but in the middle of the race I didn’t know where I was.”

By half distance it was clear that the Mercedes was not going to fade as it had done so spectacularly in Germany, setting up a tense denouement as Raikkonen, stopping twice while Hamilton and Vettel stopped three times, came into the equation.

But as Hamilton escaped, Raikkonen was left to fight off Vettel, with his much fresher tyres, over the final 15 laps. It got close, but the Finn held on to second, with Vettel was third. Mark Webber finished fourth after a strong run following his qualifying dramas, and Fernando Alonso took fifth in a less than fully competitive Ferrari, despite having Lotus’s Romain Grosjean right on his tail for the last 32 laps.

Button held on for seventh, but angrily criticised Grosjean, who collided with him on the 24th lap and was eventually handed a 20-second penalty. “Unless I’m on the grass, which is not where I want to be when I’m braking for a corner, he had no way of not hitting me,” Button said.

“It could have been a lot worse than it was. It could have ended both of our races. I was there, basically with my arm out the cockpit, going, ‘What are you doing? I’m going to be on the grass in a second.’ And I was. I don’t know what he was thinking. I don’t think he was thinking at that point.”

Hungarian Grand Prix: results and standings

Race (70 Laps):

1 L Hamilton (GB) Mercedes GP 1hr 42mins 29.445secs

2 K Raikkonen (Fin) Lotus F1 Team 1:42:40.383

3 S Vettel (Ger) Red Bull 1:42:41.904

4 M Webber (Aus) Red Bull 1:42:47.489

5 F Alonso (Sp) Ferrari 1:43:00.856

6 R Grosjean (Fr) Lotus F1 Team 1:43:01.740

7 J Button (GB) McLaren 1:43:23.264

8 F Massa (Br) Ferrari 1:43:25.892

9 S Perez (Mex) McLaren at 1 Lap

10 P Maldonado (Ven) Williams at 1 Lap

11 N Hulkenberg (Ger) Sauber-Ferrari at 1 Lap

12 J Vergne (Fr) Scuderia Toro Rosso at 1 Lap

13 D Ricciardo (Aus) Scuderia Toro Rosso at 1 Lap

14 G van der Garde (Neth) Caterham at 2 Laps

15 C Pic (Fr) Caterham at 2 Laps

16 J Bianchi (Fr) Marussia at 3 Laps

17 M Chilton (GB) Marussia at 3 Laps

18 P di Resta (GB) Force India at 4 Laps

19 N Rosberg (Ger) Mercedes GP at 6 Laps

Not Classified: 20 V Bottas (Fin) Williams 42 Laps completed,

21 E Gutierrez (Mex) Sauber-Ferrari 28 Laps completed, 22 A

Sutil (Ger) Force India 19 Laps completed.

World Championship Standings

Drivers: 1 S Vettel (Ger) Red Bull 172pts,

2 K Raikkonen (Fin) Lotus F1 Team 134,

3 F Alonso (Sp) Ferrari 133,

4 L Hamilton (GB) Mercedes GP 124,

5 M Webber (Aus) Red Bull 105,

6 N Rosberg (Ger) Mercedes GP 84,

7 F Massa (Br) Ferrari 61,

8 R Grosjean (Fr) Lotus F1 Team 49,

9 J Button (GB) McLaren 39,

10 P di Resta (GB) Force India 36,

11 A Sutil (Ger) Force India23,

12 S Perez (Mex) McLaren

18, 13 J Vergne (Fr) Scuderia Toro Rosso 13,

14 D Ricciardo (Aus) Scuderia Toro Rosso 11,

15 N Hulkenberg (Ger) Sauber-Ferrari 7,

16 P Maldonado (Ven) Williams 1,

17 V Bottas (Fin) Williams 0,

18 E Gutierrez (Mex) Sauber-Ferrari 0,

19 J Bianchi (Fr) Marussia 0,

20 C Pic (Fr) Caterham 0,

21 G van der Garde (Neth) Caterham 0,

22 M Chilton (GB) Marussia 0.

Manufacturers:

1 Red Bull 277pts,

2 Mercedes GP 208,

3 Ferrari 194,

4 Lotus F1 Team 183,

5 Force India 59,

6 McLaren 57,

7 Scuderia Toro Rosso 24,

8 Sauber-Ferrari 7,

9 Williams 1,

10 Marussia 0,

11 Caterham 0.