Sri Lanka captain Lasith Malinga elected to bat first after winning the toss and his team scored a competitive 161-9 in 20 overs, but New Zealand chased it down with two balls to spare in a tense final over.
Only 36.3 overs were possible after early rain and a wet outfield caused a delayed start and bad light resulted in an early finish.
Doug Bracewell made 44 from 26 balls and Scott Kuggeleijn, on debut, hit an unbeaten 35 from 15 and then returned to take 1/19 and 1/26 respectively with the ball for New Zealand.
Taylor made 137 and Nicholls 124 not out as New Zealand reached 364-4 batting first, highlighting the growing depth of their batting as they work towards the World Cup in England.
Sri Lanka's Thisara Perera smashed 13 sixes on his way to 140 off 74 balls against New Zealand at the Bay Oval in Mount Maunganui.
Sri Lanka made a solid start, helped by 71 from Danushka Gunathilaka. But a middle-order collapse left them facing a comprehensive defeat until Perera scared the hosts.
Guptil was straight back into the groove Thursday, compiling his 14th one-day international century to lead New Zealand to 371/7 as it batted first after winning the toss.
The home team won despite having been dismissed for 178 in the first innings, that total made competitive by lower-order batsman Tim Southee's 68. Southee was named player of the match.
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