Chasing 282, England were bowled out for 246 with 15 balls to spare with Deepti Sharma and Shikha Pandey picked up three and two wickets each.
England just about kept themselves in the hunt and were still in with a chance thanks to Fran Wilson's maiden fifty at 229 for six in the 44th over.
Mithali smacked a 73-ball 71, studded with 8 boundaries and created the record of scoring seven consecutive half-centuries in women's ODIs.
Mandhana, by this stage, had also perished, holing out to Danielle Hazell at midwicket as she climbed into a short ball from Knight and trooped off, proud but disconsolate for 90 from 72 balls.
Raj has said women's cricket struggles to get the same recognition as men's, but she believes television coverage and social-media buzz is helping.
They came unstuck against an inspired India side who are two places below them in the world rankings, in fourth, but showed more intent with the bat, more discipline with the ball and some electricity in the field.
For England, Knight scalped two wickets for 41 runs. Heather Knight (2-41) finally managed to provide a breakthrough when she dismissed Mandhana in the 27th over.
Liverpool Complete £36.9m Signing Of Mohamed Salah
Roma snapped him up on a permanent basis last summer and he repaid them with a series of impressive displays in Serie A. Mohamed Salah admits he has a "point to prove" after completing his £36.9m move to Liverpool from Roma .
England's hopes of a record-breaking victory looked to have disappeared when they slumped to 154 for five, but a sixth-wicket stand of 62 between Wilson and Brunt appeared to have turned things round.
West Indies also come into the tournament with plenty of confidence having lifted the ICC Women's World Twenty20 just a year ago, as part of a hat-trick that included the ICC World Twenty20 won by the men's team and the ICC U19 Cricket World Cup taken home by their colts.
"This game definitely makes a lot of impact for the Indian team, because posting 280 on the board this is the highest that we have posted batting first and winning against the hosts and with you so many players who are playing their first World Cup..." "We didn't bowl the way we wanted to and India put the pressure on us".
"After I batted, I realised that the wicket didn't have much assistance for the bowlers, and that the spinners, in particular, will have to bowl in the right areas".
The White Ferns then took charge as captain Suzie Bates (106 not out) and Amy Satterthwaite (78 not out) shared an unbroken second-wicket stand of 170 as eight Sri Lanka bowlers failed to separate them.
Meanwhile Saturday's other match saw 2000 champions New Zealand hammer Sri Lanka by nine wickets at Bristol. India, in a big ticket World Cup game, on TV, would have to see off any early movement, in the air and off the pitch.