England bowled India out for 134 and reached their target for the loss of six wickets with 17 overs to spare.
Holders England went into the game needing a win to keep their slim hopes of qualifying for the semi finals alive after losing their opening three matches.
England managed to eradicate the fielding mistakes, which had proved costly against the West Indies and South Africa in particular, to bowl India out for just 134, with Charlie Dean finishing with four wickets in only her second World Cup match.
Knight then steered England home with the bat as they chased down India’s below-par total with 17 overs remaining.
Tammy Beaumont and Danni Wyatt were both out for just one run to leave England starting their chase at four for two and the warning signs were there before a resurgence from Knight and Nat Sciver.
Sciver made 45 and Knight played a captains innings, seeing her side over the line as she finished unbeaten on 53.
England started with the ball as they meant to go on after winning the toss and choosing to bowl, Anya Shrubsole claimed her 100th ODI wicket, bowling Yastika Bhatra at the top of the Indian order for just eight runs.
Despite 35 from Smriti Mandhana, the wickets continued to tumble with India slipping to 28 for three then 86 for seven.
Richa Ghosh made 33 from 56 before being run out by Sciver, but it was not enough for India as they were bowled out for just 134 with 13 overs remaining of their 50.
Dean finished as the pick of the England bowlers with four wickets for just 23 runs, while Shrubsole finished with two for 20.