They are just 71 runs short of the all-time best Otago first-class partnership that Bert Sutcliffe and Les Watt scored against Auckland 59 years ago.
Sutcliffe and Watt put on an opening partnership of 373 runs in the Plunket Shield match at Eden Park in the 1950-51 season.
Haig and Broom came together when captain Craig Cumming was dismissed at 55 and took the score to 357 for two at stumps.
Haig scored his third first-class century and was 150 not out and Broom was 159 not out.
The pair also beat the best Otago third-wicket total of 227 that Ken Rutherford and Bruce Blair scored against Central Districts at Alexandra in the 1988-89 season.
The next milestone was to beat the 254 runs that Kevin Burns and Ken Rutherford scored against Wellington for the second wicket at Oamaru in the 1987-88 season.
They then passed the 266 runs that Sutcliffe and Bill Haig scored for the fifth wicket against Auckland at Carisbrook in the 1949-50 season.
"It was an outstanding effort by both players," Otago coach Mike Hessan told the Otago Daily Times from Napier yesterday.
"We still have a long way to go and I want them to stay there and get the record tomorrow.
"We have shown batting promise in our early games and our batsman have got to 50 or 60.
"The big difference today was that they stayed together and went on to big scores."
Hessan shuffled the batting order yesterday and lifted Haig to No 3 and put Greg Todd down the order to No 5.
"Shaun made the most of his opportunities today," Hessan said.
It was the third first-class century by Haig and the seventh by Broom.
Haig batted for 373 minutes and hit 19 fours.
Broom batted for 321 minutes and hit 18 fours and one six.
• Northern Districts pace bowler Tim Southee tore Wellington's first innings apart when he grabbed eight wickets on the opening day of their Plunket Shield match at Hamilton yesterday.
Wellington, with useful contributions of 69 from Josh Brodie, 88 from Cameron Merchant and 58 from Luke Woodcock, were 241 for six at one stage after tea.
But Southee ripped through the lower order to have it all out for 263.
His eight wickets cost just 27 runs from 25 overs that included 12 maidens.
It was his fifth first-class five-wicket bag and surpassed his previous best figures of six for 68 against Auckland in the 2007-08 season.
• Boosted by centuries from Michael Papps and Johann Myburgh, Canterbury took early control of its Plunket Shield match against Auckland in Christchurch yesterday.
Canterbury ended the day on 368 for six after winning the toss at Queen Elizabeth Park, with veteran former international Chris Harris finishing the day unbeaten on 83, a score that included nine fours and three sixes.
At one stage Canterbury was teetering at 51 for two.
