Although Hamilton started from his maiden pole position for his new team, and the 27th overall of his Formula One career, the 28-year-old had to settle for third behind race winner Fernando Alonso and Kimi Raikkonen.
Even that position, however, was touch and go at the death of the 56-lap race as a charging Sebastian Vettel finished within 0.2secs of the Briton come the chequered flag.
But with Hamilton standing on the podium for the second consecutive race, it is the first time a Mercedes driver has achieved such a feat for three years since Nico Rosberg in 2010.
Overall, though, Hamilton was smiling as he said: "It was a good race for me, and I'm quite happy with third.
"Of course, I would have liked to have won, but Fernando and Kimi were a little bit too fast for us.
"I was able to apply a little bit of pressure to Kimi, but not enough to get close to him and overtake, and then my tyres were shot at the end I was trying to hold off Sebastian.
"I could see his car getting bigger and bigger in my mirrors, so it was nice to be able to hang on for the third place, so I'm happy with the podium, happy with the points."
Over the team radio after the chequered flag, Mercedes team principal Brawn was breathing a sigh of relief in seeing Hamilton hang on to third, admitting "that was close".
Brawn, however, further added: "We are not quite there yet, but we are not so far away so let's keep working hard."
As for Hamilton, he knows that is true because the Mercedes appears to be down slightly on race pace compared to that in qualifying.
Hamilton added: "The guys did a great job this weekend to get us where we were - on pole and finishing third.
"We got the absolute most out of the car we had and that's very satisfying, but like Ross said, we're not quite there yet in terms of overall pace.
"I'm not really sure where we're losing out, but everyone is working so hard and I know we can do it.
"There are a couple of areas we can focus on on the car, but we also have to bring some more updates and keep on improving.
"I will also analyse a little bit and try to figure out whereabouts we're losing the time, see if we can zone in on that and try to improve there."