Experienced campaigners Michael Papps and Luke Woodcock set up the victory with a 235-run second-innings partnership for the first wicket.
That allowed their side to set the Volts a demanding target of 355.
Offspinner Jeetan Patel did the rest with six for 77. But while Neil Broom was at the crease the unlikely looked increasingly likely. He was hitting the ball nicely but his departure for 85 was a start of a rapid decline for the visiting side.
Wicketkeeper Derek de Boorder resisted with 58 but Otago's remaining batsman were unable to have a positive impact. Sam Wells, Bradley Scott, Rhys Phillips and Jacob Duffy contributed just five runs among them in a second-innings total of 262.
Otago coach Nathan King felt the match started to slip away with the rain on day two. That left Otago needing to make a bold play and it did that by declaring 49 runs behind.
But Wellington took over from there with the monster partnership between Papps and Woodcock.‘‘We went out there with the intent of bowling them out,'' King said.
‘‘It was never a case of seeing what they would leave us to chase. But right from that moment nothing went right for us with the ball.
‘‘They dictated the game from there on in.‘‘Chasing around 350 is always a tough chase no matter how many overs you have to face.''There was some brief hope when Broom and de Boorder were batting together.
‘‘They put on probably about 50 runs after tea and that was a really good partnership. But the reality was, if we lost wickets at that time, we were going to put ourselves under a lot of pressure because we were already four down.
‘‘Up until those guys got out ... we still had a chance. The run rate was manageable but it was the wickets which cost us.''
Patel took four of the last five wickets and finished with nine for the match.
On Saturday, Otago resumed on 100 for two with plenty of work ahead to get into a position to make a declaration. Wellington had posted 328 but Broom (48) and Anaru Kitchen (72) chipped away at the home side's advantage.
Otago skipper Hamish Rutherford decided his side had enough runs on the board at 279 for eight and declared.
Papps and Woodcock took over from that point. Both men made centuries. Papps was the more aggressive. His 28th first-class hundred came up off 150 balls.
He was eventually undone on 132 and Woodcock went for 131 when Michael Bracewell grabbed a catch off the bowling of Jacob Duffy.
The experienced duo got their side into a strong position and Wellington declared at 305 for four.
Otago's next assignment is a one-day match against Auckland at Molyneux Park.
