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University dominated the opening 40 minutes, scoring four tries to take a 31-3 lead into the shed. Fullback Taylor Haugh provided the spark with two tries.
He showed tremendous strength to reach out and score both of them.
But Taieri roared back into the match in the second spell with tries to captain Tom Hardy and two to beefy lock Don Lolo.
Watch the full match courtesy of Elevate Analysis
A penalty try from a scrum left the scores locked 31-31 with five minutes remaining.
But University worked its way back up field and got the winner.
In the women's final, University upset the undefeated Pirates 32-19 to defend its title.
University 38 (Taylor Haugh 2, Patrick Atkinson. Tyler Beary, Angus Williams tries; Mike Williams 5 con, pen)
Taieri 31 (Don Lolo 2, Tom Hardy, Penalty tries; Corey McKay 3 con, Josh Casey pen). Halftime: 31-3.