Deepti followed up her four-for in the previous game with figures of six for 20 to bundle out Sri Lanka for a meagre 112 in 38.2 overs. India then crossed the target in just 29.3 overs with Veda Krishnamurthy top-scoring with an unbeaten 61.
Sri Lanka got off to a good start after electing to bat, with openers Yasoda Mendis (14) and Prasadani Weerakkody (19) adding 33 before Deepti took two wickets in two consecutive deliveries to trigger a dramatic collapse.
Debutant Preeti Bose also put up an impressive show, returning figures of 8-4-8-2.
India's chase started in a shaky fashion as the home team lost both openers Poonam Raut and Smriti Mandhana cheaply.
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While Poonam was dismissed for a duck in the very first over, Mandhana was run-out soon after for six.
Veda and Deepti (28) then consolidated the innings with the duo adding 70 in 109 balls to take India closer to the target.
Brief scores:
Sri Lanka Women: 112 all out in 38.2 overs (Dilani Manodara 23, Deepti Sharma 6/20).
India Women: 114 for three in 29.3 overs (Veda Krishnamurthy 61 not out, Deepti Sharma 28).