The Indian fielders erupted in celebration at the spectacular catch, rushing towards her in joyous applause. The stunning catch resulted in India's first wicket, as Gunaratne departed for a two-ball duck.
Radha Yadav had a great outing as a substitute fielder. She held on to two more catches towards the end of the Sri Lanka chase.
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India piled up a tournament-high of 172-3 from their 20 overs before Sri Lanka was dismissed for 90 off the penultimate ball of the match.
India now have two wins in three games ahead of their final group match with six-time champions Australia on Sunday.
Just the top two teams from each of the five-nation pools make the semi-finals.
Mandhana made 50 from 38 balls with four fours and a six to register her 27th T20 international fifty.
She also shared a 98-run opening stand with Shafali Verma (43) before Kaur put on a blistering display of shot-making.
The captain reached her 13th half-century in the format off 27 balls and finished undefeated on 52 with eight boundaries and a six.
Just as important for India, Kaur showed little effect of the neck injury she had suffered in the win over Pakistan at the weekend.
In reply, Asian champions Sri Lanka collapsed to 6-3 inside three overs before Kavisha Dilhari (21) and Anushka Sanjeewani (20) put on 37 for the fourth wicket.
But they always struggled to keep up the run rate with Ama Kanchana (19) the only other player to reach double figures.
For India, fast bowler Arundhati Reddy and leg-spinner Asha Sobhana returned identical figures of 3-19 in their four overs.
The result means that Sri Lanka have no chance of making the semi-finals after three defeats.
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