Earlier in the day, New Zealand lost the toss and were asked to bat first on a green Basin Reserve deck.
The Indian seamers didn't waste too much time in slowly making their way through the Kiwi batting line-up, with Sharma looking particularly impressive as he eventually snagged career-best figures of 6-51.
His sidekick Mohammed Shami proved equally reliable as he finished with 4-70 from 16.5 overs.
New Zealand never got their innings going and their biggest partnership came for the seventh wicket when Kane Williamson (47) and Jimmy Neesham (33) added a brisk 47.
Williamson's knock was eventful as he was caught twice but both dismissals were overturned after the bowler in question had over-stepped.
His innings was crucial though as it helped New Zealand towards 200, while Southee added 32 and Corey Anderson chipped in with 24 but it was clearly a total that was below par.
With New Zealand holding on to a 1-0 lead in the two-test series, they will have it all ahead of them during the next four days.
SCOREBOARD