Sergio Perez says he knew a podium finish in Baku would be possible, but the Mexican admits he had to work hard for the result.
A five-place gearbox change penalty, due to damage he sustained in a crash during FP3, meant he started the race from seventh place on the grid.
Perez had a strong start but following his pitstop, he came under intense pressure from Lewis Hamilton.
He managed to pull away as the Mercedes driver struggled with an engine issue and quickly closed on Kimi Raikkonen, passing him on the last lap to secure third.
"I knew that the podium was possible today, but we really had to work hard for it," he said. "The key to my race was the great start I made to get around a Williams and a Toro Rosso.
"Then, in the first stint I was suffering with graining of my supser-soft tyres and we had to decide whether to wait for it to improve or to make an early stop.
"In the end, we stayed out longer, which was the right decision, but when I came out of the pits I struggled to warm-up the soft tyres and I was under big pressure from Lewis [Hamilton] behind.
"I pushed as hard as I could and opened up a gap, and then I focussed on looking after my tyres. I closed in on Kimi [Raikkonen] and I knew he had a penalty, but on the final lap I got very close to him and saw the opportunity to overtake him, so I took it.
"To be on the podium for a second time this year feels fantastic. The team has done a brilliant job and we are having an amazing year."
