Vettel emerged side by side with Hamilton, forcing the Brit off track and taking the lead again, but seven laps alter Hamilton swept past Vettel to regain the lead and maintaining it to the chequered flag.
Their race-long battle included Vettel jumping Hamilton at the start and the two making slight contact at Turn 1 after Vettel exited the pits alongside the Mercedes driver.
"After an unfortunate race for me it's important to focus and look ahead to Monaco, I'm hoping we can continue to improve and have a good fight there". I just said: "'Be careful, that was very, very close.' But I enjoyed it".
Hamilton admitted he hit rock-bottom after the incident which left him 43 points adrift of Rosberg in the championship race. (Lewis and I are) not best friends but we have a very strong connection.
"He was respectful, and still that respect stayed the same, but I think you could sense he was angry".
Hamilton and Vettel have now claimed two wins each in 2017, with Valtteri Bottas also winning his maiden F1 race in Russian Federation, which sees the Ferrari driver leading by just six points from the Brit in the world drivers' championship standings.
"A lot of the races that we do with the type of racing that we sometimes have to do, where you're saving fuel, like in the last race for example [in Russia], I couldn't push because the vehicle was overheating".
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The final stint of the race hinged on if Hamilton could make his soft tyres last long enough to prevent Vettel - on the harder medium compound - from fighting back late in the race. "This is why I race, to have that close battle with him, a four-time champ, is awesome".
Every driver, 1, 2 & 3 on the Podium, was lapped during a terrific race that saw Ferrari's Kimi Raikkonen and last year's victor, Max Verstappen, crash out on the 1st lap. This crash resulted in suspension damage on the Ferrari and the Red Bull, thus eliminating Raikkonen and Verstappen from the race. With Vettel in the lead for most of the race, Hamilton was a close second to his much respected Ferrari rival.
Teammate Bottas retired his Mercedes with a blown engine, letting the lone Red Bull inherit third place.
"I think it's dependent on what kind of race you have", he said when questioned on his heavy breathing.
"It's great to have a battle and a fight with another team is so much nicer and more enjoyable because there's no tension within our team".
"I was inside for Turn One, Kimi came from outside and tried to overtake from there", said the Mercedes driver.
Behind the lonely Ricciardo, Force India continued its impressive start to the season with Sergio Perez fourth and Esteban Ocon a career-best fifth. Fernando Alonso crossed the line in 12th - his first finish of the season - but there was more misery for Britain's Jolyon Palmer, who limped home last.
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