The visiting side did its best to hang on following its calamitous top-order collapse.
Jimmy Neesham clouted a better than a run-a-ball hundred and tailenders Mark Craig and Blair Soper batted for the best part of 20 overs in an attempt to salvage a draw.
But Seth Rance and the second new ball accounted for what remained of the resistance.
The victory, though, was set up by an undefeated innings of 207 by Jamie How and Noema-Barnett's over of brilliance.
Central resumed on 359 for three with a lead of 395. How had been stuck on 194 overnight and, once he reached the significant milestone, the home side quickly declared setting Otago a mammoth target of 412 for victory.
How's innings was aided by the fact Otago lost both opening bowlers to hamstring strains.
The Volts' chase had an early setback when Aaron Redmond was trapped lbw in the first over. But the damage was done in the eighth over as Noema-Barnett nicked out opener Neil Broom (11) and then Jesse Ryder for a golden duck.
Offspinner Nathan McCullum, batting awfully high at No 5, could not safely negotiate the hat-trick ball, getting an edge through to wicketkeeper Kruger van Wyk.
At four for 20, Otago's chances of winning were effectively over.
Despite the monumental setback, Neesham came in and played his natural game.
It was his second first-class hundred and it came off 84 deliveries.
He was eventually undone for 147, his highest first-class score.
Any personal satisfaction, though, was dampened by the result.
''I'm definitely flat. Obviously the main aim of the innings was to win the game or bat it out for a draw,'' he said.
''It does not really matter what you get individually when that sort of thing happens.''
Neesham wanted to add to his one career hundred this season and hopes the innings will set him up for perhaps one or two more this summer.
While part of Neesham's game plan was to put the pressure back on the bowlers by playing positively, the flat wicket and aggressive field setting meant runs were easy to come by.
''It wasn't really a plan to be overly aggressive but that is just sort of the way it ended up in the end.''
Mark Craig (15) and Blair Soper (four not out), who was batting with a hamstring strain and did so for more than an hour, defended stoutly for almost 20 overs as Otago appeared as if it might be able to avoid defeat.
But No 11 James McMillan, also nursing a hamstring strain, was trapped lbw first ball to bring Otago's innings to a close.
Otago (67 points) remains in second place on the competition table but Canterbury's 64-run win against Auckland means it has extended its lead to 18 points. With two rounds remaining, it is a very healthy buffer.
