Wellington took the game to Hawke's Bay early, capitalising on chances to go up 15-0 inside the opening 11 minutes, with a try through Ruben Love, before being awarded a penalty try on a lineout drive attempt.
It was a great start, and their decision to try and find space with their kicking game was proving to be effective. However, Wellington moved away from that tactic as the half went on.
Outside of a Jackson Garden-Bachop drop goal late in the half, there was no more scoring before the break as both sides struggled to get their attack in motion; be it through strong defence or poor execution.
Wellington held an 18-0 lead at the break, which seemed insurmountable given how the first half played out. That proved to be far from the case.
Hawke's Bay's attack, compounded by errors throughout the contest, finally clicked into gear when a Danny Toala linebreak set up Brad Weber for a try, before tries to Lincoln McClutchie and Josh Kaifa saw the Magpies take the lead with less than 10 minutes to play.
While Wellington had spent the majority of the second half happily kicking the ball back to Hawke's Bay, they now had to find a way back. It didn't take long for them to threaten, retrieving the kick-off and immediately playing the ball in the right end of the park.
While that attack fizzled out with a knock on deep in Hawke's Bay territory, a clearing kick gave them the ball back just outside the 22. Bringing in a contested lineout, Wellington went about their work, edging forward with carries one off the ruck, before spreading it wide to Billy Proctor. While the charging midfielder was brought down just short of the line, reserve halfback Richard Judd took the opportunity to dive over from the back of the ruck with the scrambling defence struggling to make up ground.
The try was converted, and Garden-Bachop added a penalty soon after to push the margin back to seven points.
There was another twist in the tale though. Hawke's Bay had an opportunity for an attacking lineout five metres out inside stoppage time for a chance to level the scores, but Kiana Kereru-Symes' throw was ruled not straight, and Wellington held on to claim a scrappy win.
"We talk about winning moments, and there were a few high-pressure situations there that we let slip, so that's what we'll look at at our review on Tuesday, but at the same time, we're bloody grateful to be going back to work on Tuesday," Kirifi said.
"We've worked bloody hard. We'll take that win, we're not happy with it, and the job's not done. We're grateful we get to go back to work for another week and hopefully right some wrongs."
Wellington will host Auckland in next weekend's semifinal as they entered the playoffs as the higher-seeded team.
Canterbury also progressed to the semifinals, holding off a late Northland surge.
Canterbury led 20-3 with 35 minutes to go, but Northland rattled off 13 straight points to give the hosts a scare.
Ultimately, Northland were left ruing a poor start which saw them concede two tries in the opening 13 minutes, and a late Fergus Burke penalty settled the nerves to give Canterbury a 23-16 win.
They will play the winner of tomorrow's last quarter-final between Waikato and Bay of Plenty in the semifinals.
Wellington 28 (Penalty try, Ruben Love, Richard Judd tries; Jackson Garden-Bachop con, 2 pens, drop goal)
Hawke's Bay 21 (Brad Weber, Lincoln McClutchie, Josh Kaifa tries; McClutchie 3 cons)
HT: 18-0