On an extraordinary weekend in Sao Paulo, Hamilton overcame a combined 25-place grid penalty to pass rival Max Verstappen and re-ignite his stuttering championship charge.
Hamilton reduced Verstappen’s title lead from 21 to 14 points with three races remaining and 78 points still available.
“That was one of the best drives I have ever seen in F1 by anyone,” said Hill, the 1996 world champion. “Utterly awesome.”
Hamilton responded: “It never gets old when you hear positive comments from such a great driver in Damon. I was such a big fan of his when I was younger when he was racing.
“I don’t get to say too much to Damon but I have always admired him. He has always been super-supportive so I really do appreciate the comment.
“From my own personal experience, it has been one of the most challenging, if not the most challenging weekends with the things that we have faced here.
“In terms of driving I feel like it has nearly been my best. But it is difficult to say because I have had so many races.”
Hamilton, disqualified from qualifying following a rear-wing infringement, drove from last to fifth in Saturday’s sprint race and was then demoted to 10th on the grid following his fifth engine change of the campaign. Only three are allowed.
But Hamilton was up to third by the start of lap five and then fought his way past Verstappen on lap 59 of 71 in one of the best races of the modern era.
Hamilton held the Brazilian flag aloft from his cockpit, before wrapping it around him on the podium, and then paying tribute to his once estranged father, Anthony.
“With the penalties it was the hardest weekend I had,” said Hamilton, 36.
“But my dad reminded me of 2004 when I was in Formula Three in Bahrain and I started 11th and then I finished first so this one is for him.
“I never thought I would be able to close the championship gap because things kept going against us.
“But it just shows for everyone never give up, whatever you are facing. You just have to keep pushing, never stop fighting, and that was my approach this weekend. It feels like the first because I have not won in a long time.”
Indeed, this marked Hamilton’s first triumph since the Russian Grand Prix in September and only his second following August’s summer break.
Hamilton’s Mercedes boss Toto Wolff, furious with his driver’s disqualification from qualifying for running a rear wing adjudged to be illegal by the stewards, said on the radio: “Lewis, this is how you overcome a 20-place disqualification.”
Hamilton replied: “It was actually 25, but you are right.”
The British driver will renew his championship fight with Verstappen next weekend on F1’s first visit to Qatar before back-to-back races in Saudi Arabia and Abu Dhabi in December.
“We still have a good points lead,” said Verstappen. “Today was damage limitation on a weekend where it was a bit difficult for us. But I’m confident that, in the coming races, we will bounce back.”