They lifted their intensity levels for a sublime final 15 minutes of action that netted three tries, with the winner scored deep into injury time.
Ruki Tipuna had a mixed day off the tee but slotted the winning conversion and with the eruption of noise at Brett Johnson's final whistle you would have thought you were at Te Ariki Park rather than Tauranga Domain.
It was a remarkable end to an entertaining game that Tauranga will wonder long and hard how they managed to lose after such a good lead.
To be fair, if some of their outside backs had made use of abundant first-half overlaps, notably fullback Steve Honey, the game could have been all over at halftime.
But it was only 15-7 at the break with early tries to George Honey and Dan Crowther matched by a fine team effort finished off by Chiefs squad member Chase Tiatia for Rangataua.
Bavou looked sharp from the bench and used his blistering pace to good effect to score twice for the 30-12 lead.
Adam Parr got one back for Rangataua before a brilliant individual effort by winger Teina Hika closed the gap to 30-24 with time running out.
Tiatia was heavily involved in an 80m surge from the kick-off that led to Rangataua camping in Tauranga's 22 for the final three minutes.
The pressure finally paid off as replacement Alex Jessop dived over near the posts for Tipuna to add the winning touch.
Rangataua captain and the game's dominant forward Matt Clutterbuck was justifiably chuffed with his team's effort to win a rare victory on the Domain.
"We know we have strike power across the park and we are not a team that is going to give up or let things slide," he said.
"We knew we had it in us. We just had to get the ball and hold it and try and light it up with our boys out wide.
"The key is scoring back-to-back points to work for a bonus point then work for a win.
"It is a matured side. A lot of the guys have been in the team for two or three years now and are probably coming of age now and taking on more leadership.
"We have a lot of character and belief within the side.
"I guess we have given ourselves an opportunity to play for a home semi now."
