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Rodrigues (50) and Krishnamurthy (57 not out) shared 117 runs for the third wicket as India Women scored 134 for 3 after electing to bat.
The decision seemed to have backfired when India were reduced to 17 for 2 in the fourth over with Shafali Verma (9) and captain Smriti Mandhana (7) getting out cheaply.
But the Rodrigues-Krishnamurthy duo steadied the innings and took the side to a decent total.
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In the West Indies run chase, the Indian Women bowlers produced a disciplined performance to restrict the hosts to 73 for 7 in their allotted 20 overs.
The West Indies were 13 for 2 in the fourth over and they never recovered from that. Half of their batters were out for 53 runs in the 14th over.
Opener Kyshona Knight was the top-scorer with 22 while Shemaine Campbelle remained not out on 19.
For India Women, off-spinner Anuja Patil grabbed two wickets for just three runs while Radha Yadav, Poonam Yadav, Pooja Vastrakar and Harleen Deol took a wicket each.
Brief Scores:
India Women: 134 for 3 in 20 overs (Jemimah Rodrigues 50, Veda Krishnamurthy 57 not out; Hayley Matthews 1/23)
West Indies Women: 73 for 7 in 20 overs (Kyshona Knight 22; Anuja Patil 2/3).