The sport has been deluged with complaints this season that it has become a boring spectacle due to a raft of technical changes which have seen the classic throaty roars of F1 engines replaced by hush-hush hybrids.
But on Sunday Hamilton edged his German teammate to take his first win at the Sakhir circuit and the 24th victory of his career, taking him level with the mark of Juan Manuel Fangio.
Hamilton, who also won last weekend in Malaysia, finished 1.085sec ahead of Rosberg in another triumph for the Mercedes team who have won all three races this season.
The 2008 world champion had to constantly fend off a series of bold passing moves by Rosberg who had started on pole to achieve the win while, down the field, other teams allowed their drivers to fight in close combat.
“Lewis did a good job defending but it was a massive fight out there and that’s what I’m here for,” said Rosberg.
“For racing like that. I think it was a good day for the sport, which is important, because of recent little bits of criticism.
“I think they’re all going to be rather quiet tomorrow — which is a very good thing. It’s good that us as Silver Arrows, we made it happen.”
It was a tense fight between the two men which eventually left Rosberg still on top of the standings albeit with a reduced margin.
Rosberg, the Australian Grand Prix winner, has 61 points with Hamilton on 50.
Their closest challenger is Force India’s Nico Hulkenberg who is in third place after three races on 28 points.
“Today, I knew I needed to get a good start and things generally went my way, except when the pace car came out,” said Hamilton who pipped Rosberg to the first corner and then steadily opened up a healthy nine-second lead.
But a safety car incursion on the 42nd of 57 laps after the Lotus of Pastor Maldonado clattered into the Sauber of Esteban Gutierrez saw Hamilton reeled in by the field.
“The safety car came out, we had different tyres. It was one of the most difficult races,” added Hamilton.
“I think the last time I had a race like that would probably be Indianapolis, 2007. So, a long, long time.
“Nico drove fantastically well. When you’re with you’re team-mate it’s very, very hard to make the right decisions of where to put your car, where to brake, all these different things, but yeah, it was great.”