Dazed, exhausted, but triumphant, Lewis Hamilton took another step towards a record-equalling seventh drivers' world championship on Sunday in one of the most exhausting and chaotic races of his extraordinary career.

The Formula One series leader and defending six-time champion, the only black driver in his sport, produced not only a perfectly measured drive, but also another clear message in his fight for equality and justice.

After wearing a "Black Lives Matter" t-shirt at all eight previous pre-race anti-racism ceremonies, he switched on Sunday to a t-shirt that bore the message "Arrest the cops who killed Breonna Taylor" and wore the same garment on the podium afterwards.

Taylor, 26, an African-American medical technician was shot dead in Kentucky in March this year.

"It's all a bit of daze," said Hamilton after a slow climb from his cockpit after the race. "It was like three races in one day... just incredibly tough today.

"This track is phenomenal and the heat and keeping Valtteri behind, who has been quick all weekend, wasn't easy. I was behind him at the beginning.

"With all the restarts, total focus was needed during that time. It was really, really hard.

"I think it was just the restarts, the first stint I was fine managing my tyres and I didn't really need to stop. The team were worried because Valtteri had a problem and then you see the things unravelling the next laps.

"Then the last one  -- we started on the softs which were used tyres and not knowing how long they were going to go, Valtteri appeared out of nowhere, when I saw Dani (Ricciardo) was behind and he was on it.

"There were times I was looking after the tyres and he would close up. This is a long, long straight so I didn't want him to get DRS. My heart is definitely racing. It is crazy to be here and have 90 Grands Prix (wins).

"Justice for Breonna Taylor."

After leading from the start, Bottas looked set to claim a much-needed win for his title challenge, but two poor re-starts left him chasing his team-mate home.

"It is disappointing because it was like a dream start for me for the race," said Bottas. "The start was really good and I also managed to hold onto my position at the Safety Car restart.

"It seemed like there were no more opportunities anymore after I lost the position at the second restart... That's how it goes. I will just keep pushing and try to get better. It has to turn out well for me at some point."