Patil took 3 for 36 in the first innings and then top-scored for India (54*) during the chase as the visitors sealed the match in the 16th over.
India won the toss and opted to bowl but Sri Lanka put up a competitive 134 for 5 in a match that was reduced to 17 overs a side due to rain.
Sri Lanka started strongly, with Yasoda Mendis smashing Arundhati Reddy for three boundaries in the first over itself. She continued to look in imperious touch until Patil removed her in the third over.
Patil then dismissed Hasini Perera in her second over. However, skipper Chamari Athapaththu and Shashikala Siriwardene put together a valuable 52-run stand for the third wicket.
Poonam Yadav eventually had Athapaththu stumped and Deepti Sharma removed Siriwardene. However, the hosts scored 23 runs off the last 3 overs despite Patil taking a third wicket to end the innings strongly.
In reply, India got off to a poor start when Oshadi Ranasinghe removed both Mithali Raj and Smriti Mandhana in the second over.
Out came young Rodrigues, who showed some positive intent by smashing two boundaries in the third over. But the hosts dismissed Taniya Bhatia in the next over, leaving the match evenly balanced.
Patil then joined Rodrigues out in the middle and the two put together an unbeaten 96-run stand to take India home. Rodrigues scored the winning runs, smashing a six on the fourth ball of the 16th over.
India had won the first and third T20I with the second match getting washed out. The last match of the series will be played on Tuesday at Katunayake.
India had previously won the three-match ODI series between the two sides 2-1.
Anuja PatilChamari AthapaththuIndia womenJemimah RodriguesOshadi Ranasingheshashikala siriwardeneSLW vs IndW 2018sri lanka womenwomen's cricket
First Published: September 24, 2018, 5:03 PM IST