The team huddled close, congratulating each other with handshakes and high fives at the Queenstown Events Centre.
Earlier in its Plunket Shield match against Wellington, the cause looked lost.
The visitors took charge, declaring their first innings at 391 for six, and quickly reduced Otago to 113 for five.
But a magnificent recovery, led by Neil Broom and finished off by Sam Wells, helped Otago wrestle back control and gain a lead of 80 after reaching 471.
Reduced to two front-line seamers with both Wells and Ian Butler sustaining injuries, Neil Wagner and Anthony Bullick bowled beautifully as Wellington slumped from 141 for three to be all out for 203.
Otago made light work of the 124 runs needed for victory, cantering home with nine wickets in hand.
Otago skipper Craig Cumming was undefeated on 53 and Haig had the joy of bringing up his fifth first-class half-century and scoring the winnings runs with a sweep shot down to fine leg.
Otago coach Mike Hesson described the win as a huge relief for his side.
"We've actually played some pretty good four-day cricket.
We've got ourselves in good positions in a number of games but have not been able to finish it," Hesson said.
The victory has come at a cost, with Wells injuring his shoulder and out for anywhere between a week and three weeks.
Butler has a side strain and may miss Otago's opening one-day game on Tuesday against Wellington at the Queenstown Events Centre.
Wells' injury came on the opening day and he spent most of the game on the sidelines.
He was able to bat though and shared in a wonderful partnership with Broom.
The pair put on a record 147-run stand, surpassing the previous Otago seventh-wicket record against Wellington of 143 set by Thomas Fraser and Cecil Toomey in 1939-40.
Broom posted his seventh first-class hundred and brought up 3000 runs in the process, and Wells scored his maiden century, a superb undefeated 115.
Wells had shown promise with the bat but his previous best score was just 29.
The 25-year-old University-Grange all-rounder has also been a surprise package with the ball this summer, taking 14 wickets including two five-wicket bags.
Neil Wagner also achieved a milestone by smashing his maiden 50, a hard-hit 70 from just 71 deliveries.
It featured some savage pull shots with anything short whacked over midwicket.
Having conceded a first innings lead of 80 runs, Wellington lost three quick wickets but rebounded through a 99-run stand between Josh Brodie (70) and Luke Woodcock (47).
But a double breakthrough from Otago blocked off Wellington's prospects of setting up a chase and left it with just the survival option.
With Otago down to two front-line seamers, those prospects seemed bright.
But Wagner and Bullick tore through the middle order, taking three wickets apiece.
"It was an inspired spell from both Neil Wagner and Anthony Bullick that very much got us through. When you've only got two seamers left and they are three down it could have gone one of two ways. But both those guys got stuck in and were critical in the win," Hesson said.
