They pressed and hammered but were undone by their own impatience, finally going ahead 13-9 when centre Ben Ward burrowed over on the buzzer.
But it was a different beat that emerged after the break, with the brave Opotiki side's back broken by a scintillating 90m solo try from Jack Wilson that had shades of John Kirwan at Eden Park in 1987, perhaps without the ducking and weaving but with all of JK's pace and power after sending wing Kiwi Biddle sprawling with a powerful fend just metres from his own goal line.
Fired up by coaches Craig Jeffries and Leo Scott, who implored their young pack to put their heads down and work a bit, Te Puke made light work of the second 40.
A clever chip-and-chase gave halfback Jamie Nutbrown a try and Te Puke a 26-9 lead.
Wilson and Nutbrown's efforts were scored while Opotiki wing Greg Smith was in the sinbin.
Minutes after his return prop Joseph Howe was given time on the naughty seat, with the numerical advantage again exploited when hooker Nathan Harris cruised over.
First-five Nick McCashin's missed the conversion but landed 16 points in a tidy display.
Jeffries was as stunned as anyone by Tauranga unravelling at the Domain.
This forces them to sit down and plot a finals game plan against entirely different opposition to what they had anticipated.
"We were quite keen to play Tauranga, to be fair, because we played horribly against them the last time and I seriously doubt we could put in another 40 minutes like that second 40," Jeffries said.
"But good on Rotoiti. The Wayne Ormond factor is huge with them and having Jesse Acton back gives them a superb loose forward trio.
"They're a really good side and will be as hungry as hell, imagine the week they're going to have now.
I say bring it on. I'm excited already and it should be fun."
For a while it looked like no side from outside Western Bay of Plenty would make the playoffs before Rotoiti and Opotiki sneaked in, something that Jeffries was pleased about.
"It's great to see Rotoiti emerge this season and Wayne has done some fantastic work there and is getting reward for it. Opotiki too have done a lot of work to get a good squad together and get some local boys there, Te Puna's the same, and it's good to see teams putting in the effort to get where they want to be."
Of pressing concern was Te Puke's predilection on Saturday to walk before they could run, with a lack of gruntwork up front leading to a confused effort further out, with first and second-fives McCashin and Simon Rolleston tripping over each other in the face of enthusiastic Opotiki defence and little forward momentum.
Jeffries delivered the message to his side at halftime in easy-to-understand terms.
"We just needed to play some rugby and stop getting ahead of ourselves because we were trying to be too tricky before we'd even set the game up," he said.
"We were a bit unlucky as well [with two first-half tries disallowed] but you earn the right to get flash, and that's by doing the first things first, winning the contact area and setting a platform, then getting the ball wide."
Te Puke have unlimited potential in the backline but perhaps their biggest weapon is their depth off the bench.
Jeffries and Scott are demanding a job and were served well by the injection of enthusiasm coming from the subs.
Jeffries assisted Jeremy Cotter last season as Te Puke won their first Baywide title before he and Scott grabbed the reins this year.
No pressure then to at least get the club into another final?
"Taking over as coach that was part of my thinking.
"I didn't want to be the one stepping in taking the team backwards. But we spent a lot of time getting a decent squad together, making sure there were a heap of local boys in there who were going to work hard.
"Guys like Rollo [Rolleston] and Cash [McCashin] have driven the team fitness and excitement-wise, so not only is the team benefiting but they're also getting what they deserve," he said.