Taieri had the upper hand in the first spell and led 17-6 at the break and stretched the margin to 20-6 early in the second spell.
But the Dunedin forwards then took control and kept the ball tight and were like a battering ram as they drove upfield.
The turning point came in the 56th minute when flanker Hugh Blake drove round the short side and scored wide out.
The conversion by Edwards reduced the gap to seven points and an Edwards penalty goal four minutes later put Dunedin just four points behind.
The winning try was scored by replacement wing Sione Pulu after 71 minutes.
In North Otago, Old Boys trounced Valley 41-8 at Whitestone Contracting Stadium to secure their third straight title.
Dunedin 21 (Hugh Blake, Sione Pulu tries; Liam Edwards con, 3 pen), Taieri 20 (Willis Scott, Brett Anderson tries; Hayden Parker 2 con, 2 pen). Halftime: Taieri 17-6.
