England won a top-of-the-table Group Two contest by 11 runs, handing India their first defeat of the tournament.
Thakur took wickets in each of her three overs in the powerplay and claimed two more in the final over of the innings to finish with five for 15 in seamer-friendly conditions.
But Nat Sciver-Brunt and Amy Jones scored freely during most of the rest of the innings as England posted 151 for seven. India replied with 140 for five.
"We started really well," said Indian captain Harmanpreet Kaur.
"But in the middle overs we didn't stick to our plan,” she added.
Light rain started to fall towards the end of the match.
Kaur said they were aware of the possibility of a reduced target but they were well short of the required rate.
"When you are behind you have to take charge and you lose wickets," she said.
England captain Heather Knight said it was a good sign for England that they were able to fight back after Thakur's early onslaught reduced them to 29 for three.
"We talk about batting according to conditions," she said.
"It was good after three wickets lost early to show we can still punch out a score," she added.
Sciver-Brunt hit 50 off 42 balls, sharing a 51-run partnership with Knight (28) which put the innings back on course. Jones hit powerfully in the second half of the innings and made 40 off 27 deliveries.
Smriti Mandhana gave India a strong start when she hit four boundaries off Katherine Sciver-Brunt in the third over of the Indian innings. She went on to make 52 off 41 balls.
But India struggled to maintain the required run rate against steady English bowling.
Four wickets fell to catches off attempted big hits and there was a run-out as India tried to lift the tempo.
Teenager Richa Ghosh hit powerfully towards the end, making 47 not out off 34 balls, but it was not enough to change the outcome.
England, who play Pakistan in their final group match in Cape Town on Tuesday, are virtually certain to qualify for the semi-finals.
India are also well-placed to reach the last four as they meet Ireland in Gqeberha on Monday.
Brief scores:
England 151-7 in 20 overs (N. Sciver-Brunt 50, A. Jones 40; R. Thakur 5-15) v India 140-5 in 20 overs (S. Mandhana 52, R Ghosh 47 not out; S. Glenn 2-27)
Result: England won by 11 runs
Toss: India
