The Tigers' 244 all out began to look a decent score as the Black Caps wobbled badly after cruising to 160-2 but they eventually claimed a tense victory with just 17 balls in hand.
On another day, Bangladesh might have sprung another major upset, having turned over South Africa in their opener at The Oval.
Back at the same venue, the Tigers were undone by fractional run-out calls going New Zealand's way during the run chase. Taylor's 82 batted the Kiwis into a strong position that they converted into what became a nail-biting triumph.
Photo Getty Images. Caption: Ross Taylor played the pivotal innings