Put into bat, India made 258 for 8 with the help of some fine batting from Sarfaraz Khan (74), Rishabh Pant (57) and Armaan Jaffer (46) at the Sher-e-Bangla National Cricket Stadium on Saturday.
But Mahipal Lomror stood out with a fine all-round display as he followed up his 45 with the bat with 5 for 47 to help his team skittle New Zealand out for just 138 in the 32nd over.
Seamer Avesh Kumar, who took three wickets in his first four overs to reduce the Black Caps to 5 for 3, returned 4 for 32 to be later declared Man-of-the-Match.
"Our first aim to make the quarter-finals has been realised but we cannot afford to relax. We need to top the group, so the match against Nepal will be very important.
I am confident because the batsmen are in form and the bowlers too are doing well. It is good that the seamers and spinners have got used to conditions here," said India captain Ishan Kishan.
Three other Asian sides -- Nepal, Pakistan and Sri Lanka -- also advanced to the Super League quarter-finals with their second successive wins.
India and Nepal, who took the two top spots in Group D at the expense of New Zealand and Ireland, will clash on Monday in their last league match to decide the group topper.
Nepal rode on a five-wicket haul by leg-spinner Sandeep Lamichhane -- which included the first hat-trick of the tournament -- to defeat Ireland by eight wickets and confirm their maiden appearance in the quarters.
Ireland were tied down to 131 for 9 after electing to bat and Nepal, who had stunned New Zealand in their opening match, coasted home in the 26th over with Yogendra Karki making 61.
Lamichhane had Lorcan Tucker and Adam Dennison caught off successive balls in his fourth over and then bowled Fiachra Tucker with his next delivery to complete the hat-trick.
Nepal captain Raju Rijal said qualifying for the quarter-finals meant a lot to his nation while Ireland captain Jack Tector blamed his team's low total on the regular fall of wickets.
Sri Lanka survived a tense run chase by Afghanistan before clinching victory.
Kamindu Mendis, who possesses a rare talent of bowling both right-arm off-spin and left-arm orthodox spin, claimed 3 for 36 runs.
Pakistan scored a seven-wicket win over Canada after bowling out the unfancied rivals for 178. Hasan Khan took three wickets and Shadab Khan took two.
The Pakistanis surpassed the target in the 41st over with opener Zeeshan Malik scoring an unbeaten 89 and Saif Badar 44.
Pakistan captain Gohar Hafeez said he was satisfied with the way the tournament was progressing for his team.
The 11th edition of the biennial 16-nation tournament features nine Test-playing nations and seven Associate and Affiliate Members.
Teams have been divided into four groups with the top-two in each advancing to the Super League quarterfinals and the other two qualifying for the Plate championships.