Indian women first struggled to 199 for six and then bundled out West Indies women for 184 in 49.1 overs.
Sent into bat, Indian women did not have the best of starts and found it difficult to rotate the scoreboard. They were soon reduced to 52 for three in 20.5 overs.
Krishnamurthy (71) and Harmanpreet Kaur (19) then shared 51 runs quick runs for the fourth wicket to give some momentum to Indian eves' innings.
Debutant Devika Vaidya remained unbeaten on 32 off 45 balls, while senior pro Jhulan Goswami made a 16-ball 18.
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Other notable scorers from Indian women were opener Deepti Sharma (23).
Chasing the target, West Indies women top-order made a decent start before losing the plot against Rajeshwari. The visitors were also hampered by three run outs.
Kycia Knight (55) top-scored for the visitors followed by notable contributions from Hayley Matthews (44) and wicket-keeper Merissa Aguilleira (22).
Brief Scores:
Indian women: 199 for six in 50 overs (Veda Krishnamurthy 71; Chedean Nation 2/21).
West Indies women: 184 all out in 49.1 overs (Kycia Knight 55, Hayley Matthews 44; Rajeshwari Gayakwad 4/34).