Taylor remained unbeaten on 107 while Colin Munro made 85 as New Zealand posted their highest total in the three-match series in hopes of avoiding a 3-0 whitewash.
Taylor and Munro put on 130 for the fourth wicket after Bangladesh captain Mushfiqur Rahim won the toss and elected to bowl at the Khan Shaheb Osman Ali Stadium at Fatullah just outside Dhaka.
Former captain Taylor made the most of his chances after Rubel Hossain dropped him off his own bowling on 12, hitting nine fours and three sixes in his 93-ball innings.
Munro, playing his first match in the series, led the initial charge to complete his fifty before he fell to off-spinner Mahmudullah.
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The left-hander smashed seven fours and two sixes in his 95-ball innings.
Taylor was initially sedate but accelerated after reaching his fifty off 69 deliveries.
His three sixes came in consecutive deliveries off a Sohag Gazi over as New Zealand added 73 in the last five overs to cross the 300-run mark.