"Float like a butterfly, sting like a bee. That's for Muhammad Ali," the triple world champion said over the radio after taking the chequered flag at a cold Circuit Gilles Villeneuve.
After parking up, Hamilton did an 'Ali shuffle' in another mark of respect for the former heavyweight champion whose funeral was on Friday.
"I was just floating out there, the car was really floating," he said of his 45th career victory in Formula One.
"The last 15 laps all I could do was think of him (Ali). The Rumble in the Jungle. Maybe he was watching the race. But RIP. This was for him," said Hamilton.
Ferrari's Sebastian Vettel finished second and Finland's Valtteri Bottas was third for Williams, but 46.4 seconds behind the winner.
Vettel had made a lightning start from third on the grid to blast past both Mercedes and grab the lead of the 70-lap race at the first corner.
Rosberg got alongside Hamilton, who made another sluggish start, but he refused to yield as they fought for the tight space and their wheels banged and forced the title leader onto the grass.
The collision was not on the scale of their crash in Barcelona last month, which took both of them out, but proved a huge setback for Rosberg who dropped to 10th with Hamilton staying second.
SITTING DUCK
"I am at a real loss to know what happened. Had it been a longer straight I would have been a sitting duck," said Hamilton.
Rosberg admitted he was angry at the time, but added: "That's racing. Sebastian had a great start, I had a decent one, Lewis had slow one.
"In Spain I went for the outside and made it work. Here, I went for the outside again and he did a real hard racing manoeuvre and I was off. I was (angry) at the time but that's racing."
Vettel, benefiting from the upgraded turbocharger Ferrari brought to the race, held the lead until his pitstop on lap 11 but the two-stop strategy was to prove the Italian team's undoing.
Hamilton regained the lead for the final time when Vettel stopped for fresh tyres on lap 36 and despite the Ferrari showing quicker pace at times was never in a position to mount a challenge.
"We have had a difficult start to the season," said Vettel, who locked up several times in the closing laps and said seagulls on the track had distracted him.
"I am not going to blame anybody, we took the strategy decision as a team...hindsight is always easy. The team is improving, we are seeing results quicker than anyone else. We are on the right track and I am enjoying it."
Rosberg gradually forced his way back through the field despite suffering a right rear puncture and on the penultimate lap tried desperately to overtake the Red Bull of Dutch teenager Max Verstappen for fourth.
It proved too much of a gamble as he skidded sideways and managed to retain fifth place. He has now gone three races without a podium finish.
Hamilton has taken 34 points out of Rosberg, who won the first four races, in just two weekends and will feel there is a growing momentum to his bid for a fourth drivers' crown after a difficult start to the campaign.
Finland's Kimi Raikkonen was sixth for Ferrari with Daniel Ricciardo seventh in the Red Bull.
The Australian suffered a slightly delayed pitstop when a wheel would not go on, two weeks after a similar blunder gifted victory to Hamilton in Monaco.
(Editing by Alan Baldwin)
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