Temba Bavuma scored a fighting 55* before the Proteas bowled India out for 93 to take a 1-0 series lead.
Simon Harmer and Javindra Jadeja each took four wickets at Eden Gardens on Saturday.
England and Australia begin the latest edition of the Ashes in Perth on Friday with the visitors looking to wrestle back the urn for the first time since 2015.
A fighting Daryl Mitchell century set up a tense seven-run win for New Zealand over the West Indies in the first ODI in Christchurch on Sunday.
Seamer Lungi Ngidi has been drafted into the Proteas’ Test squad ahead of the second Test against India in Guwahati from Saturday.
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