Replying to the home side's total of 132 for eight off 18 overs in the rain-affected match, the tourists were cruising at 117 for four after 15 overs when the cumulative effect of a persistent drizzle and fading light forced the umpires to call a halt to the match yesterday.
The final match is scheduled for Sunday at the same venue.
He came to the crease when Krishmar Santokie had Jimmy Neesham bowled off the inside-edge and found an able partner in Kane Williamson.
The man of the series from the Tests helped his captain put on 53 for the second wicket before he became Sammy's first wicket.
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Taylor smashed two sixes and a four off an over from all-rounder Russell that shot New Zealand so far ahead of the required rate that victory was a formality from that point.
Fletcher and Darren Bravo (30) put on 88 for the third wicket, but the excellent bowling of seamer Tim Southee (2 for 20) restricted the home side in the critical final overs of the innings.
He did have the consolation however of claiming the wicket of Fletcher just at the point where the attacking right-hander was set to accelerate even further.