Strong halfback Boogie Paki followed suit soon after by muscling over for a try he had no right to score, with stand-off Josh Weedon again converting to make it 12-0.
Combative centre Harry Paki, who had no reservations about putting up his hand in the middle of the paddock, slipped his man one-on-one to make it 16-0 before the half.
The second half opened with a classic rugby league try from Eels winger Josh Tupou.
Weedon found the large winger on the fly with a pinpoint cross kick to take the advantage out to 20-0, which was extended to 24-0 when Muller barged over from dummy half following a flowing movement.
Then the wheels fell off. The Taniwha, suddenly attacking from different angles, sprung to life and scored their first through a cross kick of their own to Tiniwaata Dickson.
Their second, spreading through plenty of hands before finding centre Joel Thompson, was a beauty, and when Dickson dotted down for his second after blowing away from the covering Weedon and chopping inside the Eels custodian, the comeback was on at 24-14.
A fourth try within the final 20 minutes to livewire halfback Mahinga Rangi brought the margin back to four points, but the Eels' slow walk back to halfway was enough to claim the points.
Otumoetai Eels 24 (Tarquin Court, Boogie Paki, Harry Kapi, Josh Tupou, Jesse Muller tries; Josh Weedon 2 cons) beat Taniwharau 20 (Joel Thompson, Tiniwaata Dickson 2, Mahinga Rangi; Pawhare Brown 2 cons)