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 were all out for 249 in 41.4 overs in reply, threatening New Zealand's total briefly — especially when Thisara Perera (80) was at the crease — before again falling short.
Paceman Lockie Ferguson took 4-40 and leg-spinner Ish Sodhi snared 3-40 in the best performance by a New Zealand bowling unit which has been under pressure at times in the series.
But so great is the depth in New Zealand's batting that Nicholls may be in danger missing selection if wicketkeeper and opening batsman Tom Latham is available.
Taylor became the first New Zealander to score 20 centuries in a single international cricket format and continued an extraordinary run of form which has seen him score 181 not out, 80, 86 not out, 54, 90 and 137 in his last six ODI innings. While he remains in the shadow of such players as Kane Williamson and the big-hitters Martin Guptill and Colin Munro, Taylor has become the heart of the one-day lineup.
"I'm always nervous at the start of my innings but I just want to sum up the situation as quickly as possible and in all three games I've been pretty happy," Taylor said. "Obviously, leading into a World Cup I think the guys have played pretty well."
New Zealand were 31-2 when Taylor went to the crease Tuesday and he built partnerships of 116 with Williamson (55) and 154 with Nicholls to lead his team to a 300-plus total for the third time in the series. The total was inflated when New Zealand scored 69 from the last five overs.
The New Zealanders made 371-7 in the first match of the series, winning by 45 runs, and 319-7 in the second match which it won by 21 runs.
As has been the case in both of the earlier matches, Sri Lanka made a bold attempt to chase New Zealand's massive totals, which were inflated by the weakness of the tourists' death bowling.
Sri Lanka scored a commendable 326 in the first match and 298 in the second, thanks to Thisara Perara's 140 from 74 balls. But on each occasion they couldn't keep up the pace needed to reach such substantial targets.
Sri Lanka were on pace early in its run chase, reaching 66 in 8.1 before the loss of its first wicket. It went on to 107 in the 15th over before the started floundering.
Captain Lasith Malinga, who led Sri Lanka's wicket takers with 3-93, sees positives in his team's performance heading towards a series in Australia and then the World Cup.
"The bowling is getting better," he said. "I think we've realized in the last three games we're going okay after 35 overs but in the last 15 overs we're not bowling well.
"Before the World Cup people have a lot of time to think about that and improve that skill. We still need to improve our middle order batting and we will be much better — we have plenty of time to work on these things."