Up until then, the first half had followed a remarkably similar pattern to New Zealand's opening game at the tournament, with a clutch of chances created but not converted.
Jai Ingham had two opportunities in quick succession after some penalty area pinball before Bevan was denied by a last-ditch tackle then headed straight at the goalkeeper from seven yards.
Singh had New Zealand's best second-half chance, taking one touch too many when played in by Ingham. The All Whites were also denied what looked to be a clear penalty with 15 minutes remaining when substitute Noah Billingsley appeared to be brought down by the Chinese Taipei goalkeeper.
At the other end, Chinese Taipei were energetic but lacked front-third quality and despite creating a number of openings, were unable to score for the second game running.
Schmid made six changes to the side which started the opening match, handing international debuts to goalkeeper Nik Tzanev and Wellington Phoenix teenager Liberato Cacace, both of who acquitted themselves well. Tzanev tipped a goal-bound header over the bar in the closing stages to preserve his side's lead.
Cameron, Bevan, Justin Gulley and Te Atawhai Hudson-Wihongi – who all came off the bench in game one – were elevated to the starting eleven, while recent All Whites regular Clayton Lewis also made his first appearance at the tournament as a second-half substitute.
New Zealand meet unbeaten hosts India in their final pool game on Friday morning (NZT), needing to win to have a chance of making the final.
New Zealand 1 (Bevan pen 36')
Chinese Taipei 0
New Zealand side: Tzanev, Gulley, Boxall, Doyle (Brotherton), Cacace, Hudson-Wihongi, Howieson, Cameron (Lewis), Singh (Payne), J.Ingham (Mitchell), Bevan (Billingsley).
Subs not used: Crocombe, Rufer, D.Ingham, Ridenton, Dyer, De Jong, Woud.