But 19 minutes of pressure in the Magpies 22 came to nothing with poor attention to detail at key moments, uncertainty in the backline and a refusal to kick penalty goals.
Halfback Te Aihe Toma then took off from a scrum 23 metres out to break the deadlock with a brilliant solo effort. Dan Hollinshead converted.
Magpies finally got some ball and halfback Brad Webber made the defence look silly twice before scoring from his second run. Ihaia West converted then kicked a penalty to give the Magpies an unlikely lead.
A final mistake by the Steamers summed up their half, with the players overly keen on pushing the pass as they chased the four tries they needed.
The Steamers needed to score early in the second stanza and they did.
Replacement fullback Chase Tiatia sparked the move with a great run in his first action since breaking his leg in the opening match, with Lalakai Foketi finishing off in the corner after 17 phases.
Joe Tupe started another raid that should have been try number three but for a forward pass.
No matter though as a minute later replacement prop Solomona Sakalia was driven over from a smartly taken 5-metre lineout. Hollinshead converted for a 19-10 lead after 51 minutes.
Three minutes later the Steamers knocked on a metre short with another try looming that may have put the Magpies out of the contest.
But the fourth came after 63 minutes through outstanding No 8 Joe Tupe, or so it seemed, but the TMO ruled an obstruction to wipe the try out in a highly disputable decision.
Surely that decision would not define the Steamers season?
Thankfully not. Their dominant scrum led to another penalty, a lineout five metres out, another penalty and lineout, then multiple drives at the line. Tupe was held up with 10 minutes left.
And then came the key moment when referee Paul Williams awarded a penalty try as the Magpies collapsed another scrum.
Leading 26-10 the Steamers had the game in the bag it seemed. But a yellow card against Henry Stowers gave the Magpies some late momentum and they scored two late tries to centre Jonah Lowe to close to 26-24 with a minute left.
They attacked again and with Bay of Plenty fans praying for a mistake, replacement flanker Matty Axtens, who has hardly played all season, intercepted a pass to finally put an end to the late renaissance by the Magpies.
North Harbour can clinch third place and push Bay of Plenty to fourth if they beat Northland in Whangarei tomorrow.
That would suit Bay of Plenty as fourth place means an away semifinal against Otago, a team they have a better record against than the other semifinal option in Wellington.
Bay of Plenty 26 (Te Aihe Toma, Lalakai Foketi, Solomona Sakalia tries; penalty try; Dan Hollinshead 3 cons)
Hawke's Bay 24 (Jonah Lowe 2, Brad Weber tries; Ihaia West 3 con, pen) HT: 10-7 Hawke's Bay
