Kavanagh took control of the game in Alexandra in the first spell when flanker Chris Vaughan and halfback Johnny Thorn scored tries to lead 18-0 at the break.
Kavanagh scored its two tries in the first 10 minutes when the forwards took control and made ground with the pick and go. This was led by hooker Joe Weatherall and prop Peter Pupualli.
Thorn controlled play and directed his forwards efficiently. Soane Amato ran strongly in the midfield.
Fullback Rhys Johnson kicked accurately and landed two penalty goals and a conversion.
Dunstan had the edge in the second spell but the strong Kavanagh defence made the game safe.
First five-eighth Hamish Cooke kicked five goals and scored 14 points to help Gore High School beat King's High School 19-12 in Gore.
Winger Hayden Stephens scored a try to give Gore the lead 13-7 at halftime. Flanker Alex Pierce was the best of the Gore forwards and lifted his game when playmaker and No 8 Morgan Mitchell was injured at the end of the first half.
King's had a powerful front row with props Ayden Lloyd and Hayden Fleury and dominated the scrum in the second spell. Ben Johnson was a lively loose forward.
But the side could not bridge the gap because it made too many mistakes and was not able to breach the strong Gore defence.
The South Otago High School forwards relished the muddy conditions when they beat Verdon College 29-10 in Invercargill.
It was only South Otago's second win in the competition after 11 rounds.
Loose forwards Jamie Sutton and Jonny Sargent both scored two tries as the South Otago pack took command.
South Otago played to the conditions and kept the ball tight. Hooker Josh Turnbull and No 8 Elliott McKinnell also had strong games. Halfback Dion Shaw made sure the ball was kept in the forwards.
Southland Boys' High School had a comfortable 48-8 win over Menzies College.
Southland Boys' plays Gore, and Otago Boys' will meet King's in the semifinals.
Otago Boys' and Southland Boys share the lead with 49 points after 11 rounds of the competition and are followed by Gore 40, King's 39, Waitaki Boys' 31, Dunstan 28, Kavanagh 22, Menzies 18, John McGlashan 14, South Otago 16, St Kevin's 9, Verdon 2.
Otago Boys' plays Waitaki Boys' in a midweek game.