Forty two years have passed since the Scot, now 75, won his third and final title in 1973 but Mercedes' double world champion is well on the road to joining him after a third triumph in four races.
Stewart was on hand to conduct the post-race podium interviews at the Sakhir circuit, congratulating Hamilton on the 'hell of a season you're having.'
He has not always been complimentary in the past, questioning the Englishman's mind management skills, as well as career and lifestyle choices, but Hamilton accepted the praise gratefully.
"It's always positive to have other real champions appreciate what you do. So it feels nice," he told British reporters.
"He said something to me in the room afterwards... he always talks about me catching him. He said 'You're going to catch me, but I'm fine with it'."
Hamilton was already Britain's most successful driver in terms of race wins -- Bahrain making 36 for his career compared to Stewart's 27 and Nigel Mansell's 31, although it is unfair to compare eras.
This season, however, he has hit a new level of performance.
He has started every race on pole and is now 27 points clear of closest rival and team mate Nico Rosberg. Sunday was his ninth win in the last 11 grands prix.
He may not be unbeatable, as Ferrari's Sebastian Vettel showed in Malaysia, but he is feeling stronger than ever.
"I feel very powerful in this car, with the package we have," he said. "I feel I am able to get everything from it. I feel more comfortable in this one than I even did in last year's.
"I feel that the power's greater than ever, in terms of strength in the car... I am getting close to my full potential. Who knows where that is but I feel like I'm extracting everything I've got."
Hamilton can now look forward to spending some time with his brother Nicolas, preparing to compete in the British Touring Car series, before Formula One's European season kicks off in Spain on May 10.
"I've got to improve when I get to Barcelona," said the Briton, who won four of the first five races last year but was still taken down to the wire by Rosberg.
(Reporting by Alan Baldwin, editing by Ken Ferris)
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