Jamieson, who was the man of the match for his seven wickets in the final, felt nervous while watching the action from the dressing room.
Chasing 139 for victory in a low-scoring match, New Zealand romped home in the final session of the reserve day, which was activated to make up for lost time in the first five days.
New Zealand reached 101/2, 116 runs behind, when bad light forced early stumps on the third day at the Hampshire Bowl.
RCB all-rounder Dan Christian revealed that when skipper Kohli asked Jamieson to bowl with the Dukes to him in the nets, the New Zealander did not fall for that trick.
South Africa-born batsman Devon Conway and left-arm spinner Ajaz Patel also received their first central contracts.
Vihari's dismissal at the stroke of tea triggered an Indian collapse on the opening day of the second Test against the Kiwis.
India lost their last six wickets for just 48 runs to be bowled out for 242 as pacer Jamieson picked up 5/45 in his second Test.
Kyle Jamieson is almost certain to retain his place in the team for the match, starting on Saturday at Hagley Oval, despite the return of Neil Wagner, who missed the Wellington game due to the birth of his first child.
The 6 feet 8 inch tall Jamieson was called into the national squad for the final two Tests against Australia but did not play.