The 22-year-old ended the first day of practice for the season-opening race with his McLaren third on the timesheets, ahead of team mate and double world champion Fernando Alonso.
Only the two Ferrari drivers, Brazilian Felipe Massa and Finland's Kimi Raikkonen, went quicker than him in the afternoon -- and both had considerable prior experience of the street circuit.
"I think he's really what we need," said Moss, the greatest driver never to win the championship after finishing runner-up four times in the 1950s when Argentine Juan Manuel Fangio was in his pomp.
"And he's shown it. I think what he did was absolutely terrific," the 77-year-old Briton told Reuters. "First non-Ferrari is fairly important, let's face it.
"He's certainly stamped his position, hasn't he?"
Triple champion Stewart meanwhile hailed Hamilton as "the best prepared first year Formula One driver that I've ever seen."
The driver, poised and self-assured in a news conference, was not allowing any of it to go to his head despite the thrill of finally making the step up to the biggest stage of his career.
'WENT SMOOTHLY'
"It was pretty amazing, coming out of the pits and coming out of the garage and going down the pit straight for the first time. I'm living my dream," he said.
"To learn a circuit when it's wet is pretty tough, especially here with it being a street circuit and there's a lot of white lines around, but it went pretty smoothly.
"It is a steep learning curve but this is testing, tomorrow is what matters," added a man, who also made history as the sport's first black driver.
Hamilton, a winner in every series he has competed and last year's champion in the GP2 support series, said he had not been overawed or stressed.
"It's a bit like any other time when you are preparing for your first race of the season," he continued.
"I haven't found it daunting or any different to any other time. I didn't expect it to be like that but I feel quite relaxed about it.
"Coming to my first day at my first grand prix, it felt pretty similar to any other test that I've done. It was like another test day, but obviously extremely special to me."
