Morgan finished with three for 23, while Dean Barlett and second 'Test' star performer Timothy Southee returning with figures of three for 33 and four for 48 respectively, after the hosts' captain A De Boorder won the toss and put India in.
For India, A Rane top-scored with 56 while Tanmay Srivastava (22) and Yo Mahesh got the starts but failed to capitalise on them to post big scores.
In reply, the Kiwi colts were 116 for two when first day's play ended early due to bad light, trailing by just eight runs with as many first innings wickets in hand.
Jeet Ravel was unbeaten on 51, in partnership with skipper De Boorder (35 not out).
The three-match series is now squared at 1-1. While India won the first 'Test' here, the hosts came back strongly to level the series at Dunedin.
India 1st innings 124 all out (A Rane 56, Tanmay Srivastava 22, Yo Mahesh 15; Timothy Southee 4 for 48, Dean Bartlett 3 for 33, Greg Morgan 3 for 23) Vs New Zealand 1st innings 116 for 2 (Jeet Raval 51 not out, A de Boorder 35 not out)