Chasing a paltry target of 174, India A were 90 for six at one stage before Shardul (40 off 32 balls) and then Karn (38 no, 49 balls) guided the team to victory in just over 32 overs.
Shardul, in fact, celebrated his India call-up by getting one for 19 in 4 overs during the New Zealand innings that folded for 173 in 44.2 overs.
What should have been an easy chase turned out to be a difficult one as Abhimanyu Easwaran (49 off 51 balls) looked the only batsman comfortable at the top of the order.
His innings had six boundaries and a six but the season's first triple centurion, Prashant Chopra (0), had another horrible outing after scoring only 13 in his first match in India A colours.
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Skipper Pant, who is in the midst of a bad patch, did not help his cause either after being cleaned up by pacer Scott Kuggeleijn for 1. He had scored 2 in his previous match.
At 133 for seven, India A needed another 41 runs with only three wickets remaining.
Karn anchored the innings in the company of Shahbaz Nadeem (7 no) to take the hosts past the finishing line.
Brief Scores: New Zealand A 173 in 44.2 overs (George Worker 39, henry Nicholls 42, Basil Thampi 3/19, Mohammed Siraj 2/27, Shahbaz Nadeem 2/34)
India A 174/7 (Abhimanyu Easwaran 49, Shardul Thakur 40, Karn Sharma 38 no). India A win series 3-0.