That, combined with Sports' lineout struggling early, would have given Whakarewarewa all the momentum had it not been for a back-pedalling scrum and a lack of discipline at the breakdown.
The second half, though, was another matter.
Sports came out playing with more pace and precision, stretching an opposition that was no longer flying up to shut the ball down before it got too wide.
A penalty and a try to flying left winger Nick Thomson early in the piece extended the advantage to 19-6, before a smartly taken try from Whakarewa-rewa's halfback Chris van der Vlugt brought his side back into the contest at 19-11.
That is as close as Whakarewarewa got, though, as Tauranga Sports continued making inroads with hard, straight running against the grain that kept defenders honest on the inside.
Gareth Brown crashed over in a handy position following another successful penalty attempt, bringing the score to 29-11 and effectively deciding the contest.
Whakarewarewa's bright spot came moments later when dangerous winger Chanse Perham burned off the cover defence to collect a nicely weighted grubber kick to score an unconverted try in the right-hand corner.
Greenway completed his double shortly after with a converted try to make it 36-16 - a fitting score in a match that Tauranga dominated for long periods.
Greenway, hailing from Sydney and in New Zealand as part of the Inside Running Academy, deflected praise relating to his double.
"The tries I scored were pretty much just out on the wing, I trusted in our patterns and the boys stayed patient," said Greenway.
He said he was excited to be playing with Tauranga Sports and noted the increase in pace and physicality apparent in club rugby in New Zealand.
Whakarewarewa coach Maurice Stone said his side were unable to get the type of ball itstan needed to be effective.
"It was a good big team against a good little team," said Stone.
"With a bit of front foot ball our backs are lethal, but we weren't able to show that today."
Te Puke Sports won their second game on the bounce away to Te Puna under lights on Thursday night, by the skin of their teeth, prevailing 22-19 in an absorbing contest.
But the two-time defending champs, without a number of key players, did it tough against an opposition which gave the ball plenty of air in the second half.
Mount Maunganui snatched victory from the jaws of defeat against Rangataua at Te Ariki Field on Friday, running out 25-23 victors after a late 60m try to Andy Devoy broke the home crowd's hearts.