Gore remains unbeaten after the 10-all draw but it has been pushed back to third.
Otago Boys' remains unbeaten and shares the lead with King's after five rounds with 24 points .
They are followed by Gore 21, Southland Boys' and Waitaki Boys' 20, Menzies College 10, Kavanagh College 9, John McGlashan and Dunstan 7, St Kevin's 5, South Otago 4 and Verdon College 0.
Kavanagh College led 5-0 at halftime after a try by Taylor Thomas, who was on the field briefly while another player was in the blood bin.
Gore scored two tries in the second spell to lead 10-5.
The equalising try came 6min from the end when halfback Johnny Thorne scored in the corner after Kavanagh had put 12 phases together.
Kavanagh had an aggressive defence that was needed to stop the wave upon wave of attacks that Gore mounted in the second spell.
A key player in the defence was openside flanker James Tomkinson, while first five-eighth Ben Willemsen and the midfield pairing of Sio Tomkinson and Guy Woodhouse provided a solid defensive wall.
Gore had a chance to win the game in the final minute when it had a penalty close to the posts.
But the first player on the spot had a rush of blood and attempted to end the game in glory by scoring the winning try.
No 8 Morgan Mitchell made ground with the ball in hand and his rugged tackling limited Kavanagh's scoring opportunities.
Other key players for Gore were Aaron Shirley, in the midfield, and lock Sam Croughher.
Waitaki Boys' scored six tries in a comfortable 34-5 win against newcomer Menzies College at Oamaru.
Waitaki was more aggressive at the breakdown and dominated the first spell when it scored four tries to lead 22-5.
It had the edge in the forwards through its scrum.
Lock Don Lolo was a force in the lineout and aggressive around the paddock and hooker Ben Carr was a little dynamo.
They have been nominated for the South Island secondary schools team.
Carr scored two of Waitaki's six tries and Lolo scored one.
Other key players for Waitaki were first five-eighth Jamie Robb and wing Steven Butler.
Otago Boys' went on the rampage to score 12 tries to beat Dunstan 72-0 at Carisbrook.
Second five-eighth Sua Tanuvasa was in fine touch and scored 22 of Otago Boys' points with two tries and six conversions.
Halfback Josh Renton directed play efficiently and the loose trio made sure Otago Boys' dominated the breakdown.
King's was equally dominant when it scored six tries to beat South Otago 38-5 in the main game at Carisbrook.
Lock Conor Kemp had an outstanding game and No 8 Petelo Faasee and hooker Dan Fowler both scored two tries.
St Kevin's College gained its first win of the season when it beat Verdon College 31-5 at Oamaru.
Southland Boys' beat John McGlashan 57-5.