Regular New Zealand opener Jesse Ryder took a knock to his hand in the field, which gave Nicol the chance to be bumped up the order to begin the innings and he didn't let Black Caps coach John Wright down.
The Cantabrian all-rounder stroked an unbeaten 108 from 131 balls in a knock that included 11 fours.
It followed on from the neat 102 he made for the Mashonaland Eagles in a Zimbabwe domestic one-day match during the weekend, when he filled in as an overseas player.
Nicol found a reliable partner at the other end in the form of Martin Guptill, who opened the batting in place of Brendon McCullum, instead of coming in at his regular No 3 spot.
Guptill compiled 74 from 97 balls, before he was New Zealand's only wicket to fall with the score at 153. McCullum ventured in at first drop to play a cameo knock of 39 as he and Nicol saw the Black Caps home in the 44th over.
Black Caps captain Ross Taylor said he was pleased to register another win after dominating both Twenty20 encounters.
"Doug Bracewell on debut started off well with three wickets; got the ball rolling really well,'' he said.
"We probably didn't squeeze them enough in those middle stages.''
New Zealand's inability to roll Zimbabwe over for a really low total after having them four down for 21 was the only disappointing facet of the game, although it was a great batting pitch and Taylor said a par score was "280-290''.
"I guess the way Rob Nicol and Martin Guptill batted was fantastic and set the platform for a nine-wicket win.''
Zimbabwe skipper Brendan Taylor told website ESPNcricinfo.com that his site had a lot to work on.
"It was a disappointing day. To rebuild from where we were was quite tough but 230 was never going to be enough. We need a decent start and our bowlers need to put them under pressure, 300 is a total we need to look at. We need to pick our game up again. "We can learn a lot from New Zealand. We are a better side than this.''
Game two is in Harare on Sunday morning (NZ time).
Scoreboard:
Zimbabwe Innings
Vusi Sibanda c B McCullum b Bracewell 5
Chamu Chibhabha c B McCullum b Bracewell 6
Hamilton Masakadza b Bracewell 0
Brendan Taylor not out 128
Tatenda Taibu c Williamson b Franklin 4
Forster Mutizwa c B McCullum b Franklin 69
Elton Chigumbura c B McCullum b McKay 9
Prosper Utseya not out 7
Extras: (2lb, 1w) 3
TOTAL: (for six wickets) 231
Did not bat: Ray Price, Kyle Jarvis, Chris Mpofu.
Fall of wickets: 1-5, 2-7, 3-12, 4-21, 5-117, 6-192.
Bowling: Kyle Mills 10-1-29-0, Doug Bracewell 10-2-55-3, James Franklin 7-0-37-2 (1w), Andy McKay 9-0-36-1, Rob Nicol 5-0-23-0, Nathan McCullum 9-0-49-0.
New Zealand Innings
Rob Nicol 108
Martin Guptill c Jarvis b Masakadza 74
B McCullum not out 39
Extras (2lb 2nb 7w) 11
TOTAL (for one wicket) 232
Did not bat: Jesse Ryder, Ross Taylor, Kane Williamson, James Franklin, Nathan McCullum, Doug Bracewell, Kyle Mills, Andy McKay
Fall: 1-153
Bowling: Chris Mpofu 10-1-46-0 (2w), Kyle Jarvis 6-0-59-0 (2w 2nb), Ray Price 10-0-45-0 (1w), Prosper Utseya 9-0-41-0 (1w), Elton Chigumbura 4-0-21-0 (1w), Hamilton Masakadza 3-0-13-1, Chamu Chibhabha 1-0-4-0, Vusi Sibanda 0.3-0-1-0.