Unicorns fullback, Matt Murtha, who played 40 minutes for his Napier Pirate Rugby and Sports premier team the previous day, scored two tries on debut for the hosts.
Centre Vailoa Kereti was another to shine for the Unicorns.
He converted all eight of their tries, was explosive on attack and destructive on defence.
Te Ahu said the Unicorns were rampant in the second half when they outscored the visitors five tries to three after trailing 24-18 at halftime.
Unicorns second-rower Raun Makirere-Haerewa collected a season-ending shoulder injury in the 10th minute of the match.
The Unicorns continue their campaign with an away game against Manawatu in Palmerston North on Sunday.