The Swiss driver benefited from the chaos ahead of him, especially the tangle between Sebastian Vettel and Robert Kubica near the end, to climb up to eighth position.
Toro Rosso's Buemi admitted he was lucky to get a point, but he felt his performance and strategy had been good.
"First race first point, so I'm very happy," said Buemi. "Maybe we had a bit of luck with the accidents, but even without that we were not too bad and our strategy worked well and I am very happy with the way my race went.
"I made a mistake when I was alongside Massa, hitting the limiter button, but when he put the KERS on you could really see the advantage it brings. I am pleased with what happened today because to get a point in the bag at the first race takes some pressure off.
"The team did a fantastic job considering that we have not had much testing time with the car before coming here. It's a dream really and not the result I expected on Friday. It shows we have a good potential."
Team-mate Sebastien Bourdais finished in ninth position after a difficult first part of the race, where the Frenchman struggled with the softer tyres.
"I had a very tough first part, as after just three laps, the Option tyres were graining," he said. "Several cars passed me so the team called me in and the second stint was not too bad. When the Safety Car came out, it was clear we had to fuel to finish.
"A few more Safety Cars would therefore have helped as I did a final stint of 36 laps and in the early part the car felt a bit like a caravan with all that fuel weight on board.
"I had a very big moment where I was lucky not to crash and then I had a seat belt come loose and I had to find a way of locking myself into position in the car. I think we should be a bit stronger in Malaysia next weekend."