Earlier in the day, Ramkumar Ramanathan sealed the tie for the hosts by thumping Tearney 7-5 6-1 6-0 in two hours in the fourth rubber before Yuki won the dead fifth rubber against Statham 7-5 3-6 6-4 in one hour and 55 minutes.
India now play second round tie at home in April against Uzbekistan, who got past South Korea in their first round away tie.
The 22-year-old from Chennai, with a singles world ranking of 276, was lifted shoulder high by all his team members after his superb show and the entire team made a lap of the stadium with the Indian tricolor.
The resounding victory for India also signaled the end of Anand Amritrajs three-year reign as the team captain as he will be replaced by Mahesh Bhupathi for the second round tie against Uzbekistan.
India had taken a 2-0 lead on the first day when Yuki Bhambri and Ramkumar clinched their singles rubbers against Tearney and Statham respectively.
New Zealand clinched the doubles rubber yesterday when Artem Sitak and Michael Venus got the better of Indian veteran Leander Paes and Vishnu Vardhan.
Ramkumar clinched a closely fought 51-minute first set and Tearney's game went to pieces thereafter as the Indian seized on the opportunities and ran away with the second and third sets.
The 22-year-old Chennai-born 276-ranked Ramkumar fired 12 aces but also committed nine double faults as compared to Tearney's 16.
The Kiwi player committed a staggering 10 double faults in the opening set, including three in the 12th game in which he was decisively broken by his Indian opponent.
The 6-foot-2-inch tall Indian youngster also had to dig himself out of the hole in two service games in which he faced break points.
He saved three in the fifth game in which he committed the first of his two double-faults with the help of his strong first serve clocked at over 200 kmph.