The Pole had a luckless 2007 season and his misfortune continued in Australia last week, where he had qualified on the front row only to be taken out in the race.
But the cards finally fell Kubica's way in Malaysia, as he jumped to third at the start and was faster than all bar the dominant Ferraris throughout the race.
"After Monza 2006 I finally managed to get another podium myself," Kubica said.
"I want to thank everybody in the team who worked very hard over the last two months to improve the car."
He said the key had been to get through the first corner intact, as he emerged in third after a wheel to wheel moment with team-mate Nick Heidfeld and Toyota's Jarno Trulli.
"I didnt have a good start because of too much wheelspin, and was fighting with Nick and Jarno Trulli," Kubica said.
"I took the dirty inside line and almost lost the car, but somehow I managed to get through the corner and overtake them.
"From this moment on I drove at my own pace.
"The Ferraris were too quick, but I was able to increase the gap from the cars following me.
"After the second pit stop I reduced the revs to save the engine and took it easy.
"I didnt feel very well all weekend and it was very hot in the car, so the last ten laps were pretty tough.
"But it all paid off with a brilliant result."
Heidfeld lost ground as he ran wide with Trulli at the start, and despite setting BMW's first ever fastest lap near the end, he could only recover to sixth.
"I have mixed emotions about todays race," he said.
"Of course Im happy to have clocked up my first fastest race lap in F1, and 11 points are also the best ever result for our team.
"The pace of the car was really, really good – about the same level as the McLaren.
"Thats all very positive and makes it even more disappointing that I only finished sixth.
"My start was very good and then I tried to overtake right on the outside in the first corner.
"Robert was on the inside, and Jarno Trulli was between us – I just ran out of room."