Matt Garbett scored the winner, racing on to Joe Bell's chipped pass with 10 minutes remaining before Ba Dun scored a consolation goal in injury time.
But fittingly, the goal that ended the New Zealand's rotten run was an own goal scored with at least one player offside.
Under heavy pressure from offside defender Michael Boxall, Zhu Chenjie headed Marco Rojas' free kick past his own keeper Yan Junling just before half-time.
However, with no VAR in use, the goal stood and the barren streak was over.
The win also ended another couple of lean streaks, earning New Zealand a first home win in six years and their first victory over non-Oceania opposition at home since 2009.
Three days after a 0-0 draw at Mr Smart Stadium in Auckland, the series wrapped up at Wellington's Sky Stadium, with the All Whites full of local talent.
Of the starting XI, 10 were either products of local academies or played for A-League side Wellington Phoenix.
The one without a capital connection - striker Greive - may never want to come back.
The Auckland-raised and Scottish-based 23-year-old had the chance to end New Zealand's scoreless run just after the half-hour mark when Lu Shaocong barged into Elijah Just for a penalty.
Greive stepped up for the spot kick and side-footed straight to Yan with such a tame effort that if the Chinese gloveman were a set of cricket stumps, he may not have dislodged the bails.
Fans among the 10,307 in attendance may have wondered if New Zealand would ever score again.
Thankfully, Zhu did the hard work for them, giving the Kiwis a deserved half-time lead.
China - back in action for the first time since July 2022 with this series - enjoyed their best spell around the hour-mark, with pacey pair Ba and Wu Lei spurning opportunities from through-balls.
Ba's 92nd minute strike, a terrific header from fellow substitute Sun Guowen's cross, came too late to truly worry the All Whites.
New Zealand fully merited their win, dominating possession (60 to 40 per cent) and shots (17 to 9).
Interim manager Darren Bazeley found time to hand centre-back Kyle Adams a senior debut off the bench, following Callan Elliot's first cap earlier in the week.
