With this victory, India Women have taken a 1-0 lead in the three-match T20 series.
Opting to bat, India Women posted 130 for six and then managed to restrict Sri Lanka to 96 for seven in 20 overs.
Indian eves did not have an ideal start as they lost skipper Mithali Raj (3) and V R Vanitha (12) early to be reeling at 15 for 2 in four overs.
Left-arm spinner Sugandika Kumari was the pick of the bowlers for Sri Lanka. She accounted for the top three and ended with figures of three for 28.
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Chasing a modest target, Sri Lanka lost opener Yasoda Mendis for eight with Anuja striking in the very first over. In her second over, Anuja returned to dismiss the other opener Chamari Atapattu for a duck to reduce the visitors to 13 for two.
Wicketkeeper-batsman Dilani Manodara was the only one who offered some resistance with a crucial 41 off 44 balls that included three hits to the fence.
The next-best score was captain Shashikala Siriwardene's 18 off 29 balls.
Even as Anuja finished with career-best figures of three for 14, each of the Indian bowlers came up with an economy rate of under 5.80.
Brief scores:
India Women: 130 for six (Harmanpreet Kaur 36, Smriti Mandhana 35; Anuja Patil 22; Sugandika Kumari 3/28).