Broom punched a Trent Boult delivery to the boundary to become the eighth Otago batsman to reach the milestone, joining Bert Sutcliffe (5), Roger Blunt (2), JR Reid, Matt Horne, Ken Rutherford, Ian Rutherford and Rob Lawson.
Otago declared immediately after Broom's feat at 438 for eight. That left the visitors chasing a target of 365 from 72 overs.
After 36 overs they were 120 for one.