Rangataua's forward pack had the edge in the set pieces and were well led in the loose by Matt Clutterback but they were not able to do much with the ball they won.
Greerton's win moves them up the table into a share of fifth on 16 points with Rangataua. Both clubs are still well in the hunt for a semifinal spot.
Greerton coach Kevin Lee was happy with the win and recent performances after losing the opening three games without a bonus point.
"We were right at the bottom and just have to keep clawing our way up. Game by game we have to try and win and get bonus points and see where it ends up at the end of the season,' he said.
"If it means we don't make the semis because of those three losses then so be it, but we have done the best we can since then."
Tauranga Sports (30) and Te Puke Sports (27) remain firmly in the top two spots after expected easy wins over the competition lightweights. Rotoiti (21) defeated Whakatane Marist 55-24 to stay third while Mount Maunganui Sports beat Whakarewarewa 31-20 at Blake Park to clinch fourth spot.
Mount Maunganui opened the scoring in the opening minutes through Matt Axtens and led 19-10 at half time before scoring twice in the second spell to dominate the game.
Whakarewarewa scored a late try to close the gap but have now slipped back to seventh place.