Set a target of 444, Otago got into a position to launch but its chase was derailed by a the loss of four wickets for nine runs.
Brad Wilson scored 107 and Michael Bracewell (65) and Neil Broom (84) made fighting knocks.
Then left-arm seamer Craig Smith batted for more than 90 minutes to stave off defeat.
The draw has relegated Otago to last place in the Plunket Shield. With four rounds remaining, it trails competition frontrunner Auckland by 43 points.
Otago resumed on 38 for none with salvaging a draw at the forefront of the its thoughts.
Opener Anaru Kitchen could not add to his overnight score.
He perished for 19 in the third over of the day having tickled a delivery from Lockie Ferguson through to the keeper.
That was Otago's only setback in a good morning session for the visiting side.
The in-form Wilson and an equally determined Bracewell guided the Volts to lunch at 134 for one.
The pair put on 126 for the second wicket before Bracewell hit a drive to Colin de Grandhomme.
But Broom dropped anchor and at tea the Volts were still well-placed at 213 for two.
Wilson was closing in on his 10th first-class hundred and suddenly an unlikely victory did not seem so far away.
Otago needed 231 from 38 overs and there was a change of intent after the break.
The batting was more aggressive.
Wilson's earlier patience was rewarded when he brought up his 100 from 225 balls.
But having lifted the tempo he reached for a wide delivery from Donovan Grobbelaar and sliced a catch to first slip on 107.
What was a hiccup quickly turned into a stumble and then a fall.
Grobbelaar trapped Jimmy Neesham lbw for one and drew Derek de Boorder into a false shot.
Then all-rounder Sam Wells nicked out.
The loss of four wickets for nine runs effectively brought the chase to an end.
Broom and Smith were left with the job of seeing out the remaining overs and securing a draw.
Broom was undone with the end in sight but there was no further drama.
● Canterbury chased down a paltry target of 89 to beat Northern Districts by eight wickets at Seddon Park yesterday.
Experienced allrounder Andrew Ellis helped set the win up with a 143 in Canterbury's first innings and took three-second innings wickets to complete a strong performance.
● Part-time left-arm spinner George Worker helped Central Districts seal a tense 87-run win against Wellington with a four-wicket haul at McLean Park yesterday.
Earlier in the match he scored 123 - his fourth first-class 100 this season - to help get his side into a strong position.
Black Caps limited-overs wicketkeeper Luke Ronchi almost helped salvage a draw.
He blasted 88 from 111 balls but got out late in the day leaving the last pair too long to survive.
Wellington was all out for 281.
