Mithali Raj and Co recorded their fourth win on the trot as they defended a respectable 232/8 by restricting the island nation to 216 for 7.
The Indian eves also maintained a clean slate against their sub-continental neighbours since the 2013 World Cup, having never lost a single ODI in all meetings.
India's battery of slow bowlers have choked the opposition time and again during the tournament so far.
India vs Sri Lanka, ICC Women's World Cup 2017 - As It Happened
It was no different on the day as leg-spinner Poonam Yadav (2/23 in 10 overs) led the charge with twin blows, removing the dangerous Chamari Atapattu (25) and opener Nipuni Hansika (29).
Left-arm spinner Ekta Bisht (1/48 in 10 overs) and off-spinner Deepti Sharma (1/46 in 10 overs) were also economical.
The seasoned Jhulan Goswami (2/26 in 8 overs) was parsimonious as ever, and provided important breakthroughs too.
Dilani Manodara Surangika (61 off 75 balls) batted well but found little support at the other end.
Skipper Raj marshalled her resources well after another impactful half-century, which was largely responsible for the decent total.
"In the middle overs we really pulled ourselves and the dot balls pushed them to score in the end. Overall, our spinners did quite well," Raj said after the match.
She admitted that having pure all-rounders have helped their cause while bowling.
"Cricket has evolved over the years because now we need to have more all-rounders, with bowlers who can bat in the slog overs and batsmen who can pick some wickets," she said.
The skipper praised the current batting line-up which gives her freedom to play her natural game.
"I have always enjoyed batting and stepping up when it's required. I'm blessed to have the kind of openers and I can play probably a bit of my own game which I have had to hold up
because of the kind of the responsibility I have had over the years," she stated.
The match decisively swung in India's favour when the pint-sized Poonam, coming round the wicket, got the better of Atapattu with a flighted delivery that she tried to sweep but missed the line to be bowled.
Another identical delivery saw Nipuni make a big stride forward for a slog sweep only to be stumped by Sushma Verma. The Lankan innings never had the momentum and only one team could have won from that situation despite gallant effort from Surangika.
Earlier, Deepti Sharma and Raj hit fine half-centuries to help India post a decent 232 for 8.
Deepti made 78 off 110 balls while Mithali (53 off 78) continued her good form with yet another 50 plus score to set the base for India's total after the early dismissal of openers Punam Raut (16) and Smriti Mandhana (8).
Middle-order batters Veda Krishnamurthy (29) and Harmanpreet Kaur (20) stitched crucial 50 runs in just nine overs to help India get past the 230-run mark.
Player of the match Sharma said: "The wicket was a bit slow when I batted so I adjusted accordingly by taking my time and it paid off. I tried to time my straight-bat shots properly instead of hitting them hard."
Electing to bat, India didn't have the best of starts as Mandhana departed early. She was soon followed by Raut in the 11th over that brought Mithali and Deepti at the crease.
The duo first resurrected India's innings and opened up once they got their eyes in.
They shared vital 118 runs for the third wicket to not only steady India's innings but create the perfect launchpad for others to follow.
But just when it was time for the Indian eves to launch the attack on Sri Lankan bowlers three quick wickets dragged them back.
After the dismissal of Deepti in the 37th over, Jhulan Goswami (9), who was promoted up the order, and Mithali to fell in sucessive balls of Inoka Ranaweera's 39th over to put brakes on India's scoring.
But Veda and Harmanpreet took the onus upon themselves to keep up the ante before both got out in consecutive balls in the 49th over off Sripali Weerakkody to hand the Sri Lankan right-arm medium pacer, an opportunity to claim a hat-trick.
The Indian willow-wielders managed a decent 62 runs off the last 10 overs.
For Sri Lanka, Weerakkody (3/28) was the pick of the bowlers while Inoka Ranaweera (2/55) also returned with two crucial wickets.
Ekta BishtHarmanpreet KaurICC Women's World Cup 2017ICC Women's World Cup Live ScoresIndia vs Sri lankaIndia vs Sri Lanka Liveindia vs sri lanka live scoreLive Cricket Scoremithali rajsmriti mandhanaWomen's World Cup 2017
First Published: July 5, 2017, 10:44 PM IST