Shankar then hit an unbeaten 80-ball 87 and added 116 runs for the fifth-wicket with Ishan Kishan (47 off 43). Iyer scored a run-a-ball 50 as India A returned to overhaul the stiff target, scoring 311 for six with one over to spare and take a 1-0 lead in the three-match series.
Chasing, Mayank Agarwal and Shubman Gill forged a 61-run opening partnership before falling three overs within each other.
Skipper Manish Pandey then shared a 85-run stand with Iyer but both were dismissed in the space of three balls by pacer Hamish Bennett, leaving India A at 158 for two in the 26th over.
Kishan and Shankar took the team close to victory with a century stand.
Shankar, who blasted 12 fours and a six in his 80-ball innings, took the team to victory after losing Kishan in the 43rd over. Krunal Pandya also lost his wicket in the 49th over.
Earlier, Rutherford and George Worker added 83 for the opening partnership, before wicketkeeper Seifert and Neesham shared a 82-run stand for the fifth wicket.
Among Indian bowlers, Siddarth Kaul was the most expensive as he took two wickets for 74 runs, while Shankar (4-0-12-0) conceded less than five an over.
India A: 311 for 6 (Shankar 87 not out, Iyer 54; Bennett 2/65) beat New Zealand A 308 for 6 (Neesham 79 not out, Rutherford 70; Siddarth Kaul 2/74) by four wickets.
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