Zimbabwe struggled from the opening delivery after Mayank Yadav struck with the first ball of the match, removing Brian Bennett. The hosts never recovered from the early setback and finished on 125 for 7 from their 20 overs.
Ryan Burl top-scored with 26, while Wessly Madhevere added valuable late runs.
India's bowlers kept the pressure on throughout the innings. Mayank Yadav and Prince Yadav claimed two wickets each, while Ravi Bishnoi and Shivam Dube also chipped in to restrict Zimbabwe to a below-par total.
The tourists made light work of the chase thanks to a superb innings from teenage opener Vaibhav Sooryavanshi, who produced a brilliant half-century to become the youngest player to score a fifty in international cricket.
Ishan Kishan also made an important contribution before captain Shreyas Iyer guided India home with an unbeaten knock as the visitors sealed victory with ease on 126 for 3.
India's disciplined bowling display and confident batting performance put them 1-0 up in the three-match series, while Zimbabwe will need a much stronger all-round effort to level the contest in the second T20I.
Vaibhav Sooryavanshi will return to familiar surroundings when India begin their three-match T20I series against Zimbabwe in Harare on Thursday with the teenage opener looking to revive his international form.
India captain Shubman Gill feels his team need to drastically improve their fitness record if they want to be one of the leading contenders at next year's ODI World Cup.
BCCI secretary Devajit Saikia insists Rohit Sharma remains part of India's plans in the ODI format despite reports that the final game of the series against England on Sunday could be his last.
Joe Root was sublime for his 99 not out that guided England to a four-wicket win over India in the second ODI of the three-match series in Cardiff on Thursday.
