Electing to field, New Zealand restricted India to 9-249 with Matt Henry (5-42) leading their superb bowling display, backed up by their characteristic sharp catching.
Shreyas Iyer (79), Axar Patel (42) and Hardik Pandya (45) scored valuable runs but India still settled for a below-par total.
Chakravarthy's spin then brought him a terrific haul of 5-42 as he did most to help India bundle out the Black Caps for 205 despite Kane Williamson's classy 81 and maintain their unbeaten run in the tournament.
India, who topped Group A, will now face Steve Smith's Australian team in the first semi-final in Dubai on Tuesday, before New Zealand take on group B winners South Africa in the second match in Lahore on Wednesday.
"New Zealand are a good team, who are playing some good cricket," India captain Rohit Sharma said.
"Very important to get a good result, we played a perfect game."
India did not start well though and slumped to 3-30 in the seventh over following Henry's two-wicket burst in the powerplay.
The seamer removed Shubman Gill lbw and dismissed Virat Kohli when Glenn Phillips, who's been outstanding in the field all tournament, took a breathtaking catch at backward point leaving the batsman crestfallen.
In between those dismissals, Rohit, who often leads India's powerplay assault, mistimed his pull shot against Kyle Jamieson and returned to pavilion.
Iyer and Axar forged a 98-run stand to steady India before both fell in quick succession.
Pandya produced a run-a-ball cameo down the order but India still fell short of the 250-mark.
All-rounder Pandya returned to remove Rachin Ravindra for six in the fourth over of the New Zealand innings but Williamson kept them in the hunt.
India substituted pacer Harshit Rana with Chakravarthy and the spinner made an immediate impact in his first match of the tournament that earned him player-of-the-match award.
India's spin quartet, who went on to claim nine of the 10 New Zealand wickets, put the squeeze on in the middle overs with Chakravarthy running through the middle and lower order.
"India controlled the middle phase better," New Zealand captain Mitchell Santner said.
"It spun a bit more than we thought, and they squeezed us well with four quality spinners."
