Resuming at 531 for five on the fourth and final day, India colts added 35 runs for the loss of two wickets before declaring at a massive 566 for seven at Bert Sutcliffe Oval.
Set to score 391 for an unlikely win, hosts' opener Jeet Raval compiled a solid 89 to frustrate the Indian bowlers.
Though New Zealand wickets fell in regular intervals and the visitors threatened to run through the middle order, the hosts held out for a draw, scoring 231 for six in 96 overs.
Earlier, Indian top order found their touch after being shot out for a paltry 124 in the first innings and each of them contributed in the second essay though Srivastava and Rahane's centuries swelled the total.
R Teja (50), V Kohli (54), B Sumanth (30) and S Sharma (35) were among runs, but the Indian bowlers ran out of ideas to bowl out the hosts batsmen for a series-clinching victory.
Piyush Chawla and K Appana cliamed two wickets apiece while Ishant Sharma and A Rahane took one wicket each.
The two teams will now play a three-match ODI series, beginning at Bert Sutcliffe Oval on Wednesday.
They will play the remaining two matches on February 8 and 10 at the same venue.
India colts: 124 all out and 566 for 7 decl (A Rahane 179, Tanmay Srivastava 170, V Kohli 54, R Teja 50; T Boult 2 for 91) Vs New Zealand colts: 300 all out and 231 for 6 (Jeet Raval 89; Piyush Chawla 2 for 62, K Appana 2 for 59)