When she took the baton on the last of the four laps Columba College had a 15-second lead over Otago Girls' and St Hilda's was 30 seconds behind the leaders.
Greene, who finished runner-up at the world secondary schools cross-country in Slovakia last year, scorched around the last lap in 6min 21sec to give St Hilda's a 21-second win over Columba.
St Hilda's won with a time of 30min 04sec and Columba College and Otago Girls finished with 30min 25sec.
Greene had the fastest lap time of 6min 21sec and was followed by her training partner Laura Carruthers (Columba) 6min 53sec and Anna Kean (Otago Girls') 6min 57sec.
The St Hilda's team of Jarriet Keown, Esther Fogarty, Aleisha Ruske and Meg McKay won the junior girls race in a time of 31min 18sec.
The fastest lap time was run by Charlotte Cahill (Columba) in 7min 31sec.
The Otago Boys' team of Tom Wardhaugh, Nick Elder, Chris McNoe, Hamish Cooper, Michael Ogle and Jared Hewitt won the senior boys race in 39min 06sec from Kings 40min 09sec and John McGlashan 40min 21sec.
Otago Boys' also won the junior boys race in 40min 51sec. The team was Josh Vou, Mike McKay, Bailey Brandham, Jesse Scott, Ben Wardhaugh and Reuben Scarlet-McRae.
The Kavanagh College team of Charlotte Homan, Cairan Jansen, Shauna Pali and Sam Bremer won the senior mixed race in 28min 15sec.
The East Otago team of Sam Porter, Olivia Ollerenshaw, Bridget Collins and Oliver McLelland won the junior mixed race in 29min 46sec.
