McIntosh reached the milestone in just his third test innings, spending more than 7hr grafting 136 from 337 deliveries, including 21 boundaries.
The 29-year-old opener was patience personified, but once he departed New Zealand frittered away an opportunity to build a substantial first-innings lead.
Its last six wickets tumbled for just 55 runs in less than 20 overs as the West Indies seam attack finally thrived in overcast conditions.
New Zealand had to settle for an initial lead of 64 after being limited to 371, an advantage reduced to two before stumps were drawn 14 overs early due to bad light.
Chris Gayle, with 36 not out, and Sewnarine Chattergoon plundered 50 from the first seven overs but the West Indies captain retreated into his shell after New Zealand's spinners experienced success.
Jeetan Patel had Chattergoon caught at slip for 25 while Ramnaresh Sarwan's dismal tour continued when he was adjudged leg before wicket by third umpire Mark Benson for one after Daniel Vettori queried Rudi Koertzen's initial refusal.
Xavier Marshall, on nought, is the other not out batsman.
The double breakthrough possibly tilted the balance New Zealand's way after its middle and lower-order batsmen failed to impose themselves.
Comfortably set at 316 for four, New Zealand lost three for three inside 18 balls.
Jerome Taylor triggered the slide when McIntosh was deceived by a slower ball.
He also had Brendon McCullum caught at the wicket for 31 before all-rounder James Franklin registered a nine-ball duck.
Edwards was not party to that flurry of wickets but scythed through the tail to finish with seven for 87 from 29.4 overs.
It was the 26-year-old's seventh five-wicket haul in 36 tests.
McCullum and Jesse Ryder were both culpable for New Zealand failing to occupy a position of strength on the back of McIntosh's sterling service.
McIntosh should have been caught by either Edwards or Ramdin when on 14 on Saturday, a comical fielding lapse when he skied a pull shot no laughing matter for the tourists as the cautious left-hander slowly but surely passed 50 off 181 balls.
He accelerated noticeably yesterday when resuming on 62, requiring 104 extra deliveries to reach three figures.
He raced through to three figures by employing his favoured boundary options.
McIntosh needed just 14 balls to advance from 88 to 103 as he adopted a scoring rate more associated with Ryder, his partner at the time.
Ryder helped add 100 for the third wicket but squandered a chance to reach three figures himself when an Edwards delivery took a thin edge to Ramdin's gloves.
Ryder scored a casual 57 from 68 deliveries with eight boundaries, after Ross Taylor was dismissed for four to the second ball of the morning when becoming Edwards' third victim.
New Zealand added 121 in the opening session after resuming on 145 for two before the strokemakers contributed to their own downfalls.
McCullum at least got under the West Indian's skin, his ploy of advancing down the pitch as Daren Powell steamed in infuriating the Jamaican.
Aggrieved, Powell ran through the crease and then chucked the ball past a bemused McCullum towards first slip, a response that prompted an angry exchange after he was no-balled.
While the West Indies were not penalised for giving McCullum an early let-off, Edwards admitted McIntosh's reprieve McIntosh took some gloss off his achievement.
"I guess it cost us in a big way; he got a big century," he said.
Still, Edwards felt the game was still up for grabs.
"I think it back at square one.
"If we can go and get a big total it will be good for us but they're still in a good position.
"Let's call it even stevens."
