Whiting, Greene, Kim Hebert-Losier and Shireen Crumpton won the 4x1500m event in 19min 30sec.
Their time smashed the record of 19min 46sec set in 1989 by the Leith team of Leanne Durry, Mary-Anne Henzell, Lisa Pollock and Fiona McKee.
Hill City had previously come close in 2006 when Otago and national champions Kellie Palmer, Maria Akesson, Courtney Quirin and Anna Begg equalled the record.
Race records are a treasured possession with Lovelock teams, with the men's A grade mark of 24min 12.6sec having stood since 1971.
For Crumpton, being part of a record-setting team has been a long time coming, as she has been a significant part of the success achieved by Hill City women's teams since the 1989 mark was established.
"It feels pretty good, really," she said of the team's success.
Whiting, on the first leg, had to hold out a strong challenge from Otago University's Maddie Munro, while Greene then faced another strong challenge from Otago University's Cassi Knight.
Both Greene and Knight recorded the fastest time of 4min 46sec, with Whiting third-fastest in 4min 49sec.
The challenge kept coming from Otago University runners on the final two legs, but Hebert-Losier and Crumpton held on with dogged determination to ensure their team finished 17sec clear of the field.
Otago University, which became just the fourth team to crack 20min, recorded 19min 47sec to place second, while the University of Canterbury was third in 20min 3sec.
Victory celebrations almost spilled over into the men's 6x1500m A grade, when the Hill City team of Oliver O'Sullivan, Alex Gorrie, Mike Wakelin, William Scorgie, Campbell Garry and Elliot O'Sullivan led the event.
James List then catapulted Ariki into the lead and took it to victory in 25min 43sec, finishing 9sec clear of Hill City, with Caversham third in 26min 1sec.
Ariki had an uninterrupted reign of seven years until the University of Canterbury won the title in 2006 and successfully defended it until Saturday.
Both teams were missing a list of top runners, and going into the event the Caversham young guns appeared favoured, with Hill City left unnoticed.
Callan Moody got Ariki away to a safe enough start on the first leg, but Greg Brockbank, Nathan Baxter, Dougal Thorburn and Chris Weddell had a fight on their hands to stay in touch with Hill City and set up the opportunity for List to secure the victory.
