"It's like on Christmas Day, I never expect anything," the Briton told reporters. "When you find you've got some gifts from people that love you, it's a surprise."
Hamilton started the race 21st after being hit with a 55-place grid penalty for exceeding his permitted allocation of engine components.
He played down expectations after qualifying on Saturday, saying that making it into the top-10 points-scoring positions would be a tough ask while his Mercedes team predicted an eighth-place finish.
But circumstances fell into place for the 31-year-old on Sunday.
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Hamilton made a clean start and rose through the field to fifth on durable medium tyres as drivers peeled off into the pits under the safety-car period prompted by Kevin Magnussen's massive crash.
The subsequent red-flag stoppage allowed the Briton to take on fresh tyres without any penalty before he capped his progress up to the final podium spot with some spectacular overtaking moves.
"That was perfect for me," said Hamilton, winner of six of the last seven races leading up to Spa.
"I definitely wasn't expecting that and there have been races I've done where I've needed something like that and it's not happened. It's been a real tough, tough fight from the back."
Hamilton suffered reliability woes early in the season and has long been aware he would have to take a hefty engine-related penalty.
Mercedes opted to take the hit this weekend at the 7km long Spa circuit and fitted three new power-units beyond his permitted allocation, expanding the pool of engines he can use over the final eight races.
Hamilton has been relaxed all weekend despite the prospect of starting near the back and was upbeat after Sunday's race, even though victorious Mercedes team mate Nico Rosberg cut his championship lead to nine points.
"To come out with a clean race like I did and only lose 10 points and have three new engines, it's a super bonus," said the Briton.
(Editing by Tony Jimenez)
