Midfielder Quinn Tupaea proved to be a handful in the first half for Waikato and was rewarded with a try of his own.
Otago got on the board through the boot of Josh Ioane, who blasted two penalty goals, but a late try in the half to Matt Lansdown gave Waikato a comfortable 19-6 lead at halftime.
However, the gap was closed early in the second half when Otago loose forward James Lentjes scored in the corner. With Ioane slotting the conversion to bring Otago back within six points, the visitors were back in the game – for all of seven seconds.
Waikato winger Tyler Campbell pushed the gap back out immediately from the kick-off when Otago's poorly judged attempt to bring in the ball fell into the Waikato winger's hands with a clear run to the tryline.
A second try to Reece midway through the half all but closed the door on any hope of an Otago comeback, which wasn't made any easier by Waikato dominating the possession.
In the end, the Mooloos were too strong and sealed a well-earned win.
Waikato 36 (Sevu Reece 2, Quinn Tupaea, Matt Lansdown, Tyler Campbell tries; Fletcher Smith 4 cons, pen)
Otago 13 (James Lentjes try; Josh Ioane con, 2 pens)
HT: 19-6