Great question — answering as the UphillTech team:
Finally I was able to identify this movie. It is High and Low released in 1963 and from none other than Akira Kurosawa. Original Japanese version is Tengoku to jigoku. The plot of this movie is there in Wikipedia which matches the plot in my question. Also I have confirmed the movie by watching the trailer in Youtube: As I said in the question, I had a feeling that the movie is a classic. I also felt that it was Japanese, though I wasn't sure of it. I googled for "Classic Japanese Movies" and read the plot of all movies that come up in the list. I also tried to watch the trailer of each of those movies. That led me to the correct movie and it took around 90 minutes. And it saved me from a...
Full answer by Krishnabhadra: https://movies.stackexchange.com/a/64156 (CC BY-SA 3.0).
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