After the sides were tied 20-20 at the end of normal time, the difference was the determination of Wellington's defence under prolonged pressure.
It was the replacement first five-eighths Callum Harkins, who blasted a 40m penalty goal 11 minutes into extra time to break the deadlock.
A penalty goal to level the scores was not enough for the Bay as they knew Wellington had scored one more try, and if they were tied at the end of extra time, that would give Wellington the win.
That pressure resulted in the Bay coughing up errors and having to restart their build-ups, and in the end, the hill was too high to climb.
It was an outstanding final with some prodigious personal contributions. Flankers Du'Plessis Kirifi and Brad Shields led superbly. Second five-eighths Riley Higgins and centre Peter Umaga-Jensen were controlled in midfield.
For the Bay, lock Naitoa Ah Kuoi and flanker Joe Johnston contested all the way with their rivals, while halfback Te Toiroa Tahuriorangi was outstanding, controlling the wealth of phase distribution he was required to dispense.
Aerial conditions were testing, akin to many a game played in the city's previous ground, Athletic Park, but the surface was good.
Playing with the wind, Wellington was quick to take advantage, working the ball among the pack to test the Bay defences. But when it was moved to the blindside, Shields broke hooker Kurt Eklund's tackle and passed outside to wing Julian Savea running the line. He was too strong and powered across in the corner in the fourth minute.
Bay of Plenty managed to hold fast and finally got into Wellington territory. While frustrated to have a 14th-minute try to wing Leroy Carter, playing at dummy half, disallowed when he lost the ball on the line, their patience was rewarded three minutes later.
Wellington looked to clear the line, but a kick by halfback Kyle Preston was partially charged and taken by Eklund, who charged at the line to set up a ruck from which prop Aidan Ross scored, although the referee took help from the TMO to ratify.
Savea was in the action again, this time on the right wing side, after some tidying work in midfield by fullback Tjay Clarke, who secured the ball and passed to first five-eighths Jackson Garden-Bachop, who transferred quickly to Savea. He set sail for the line with only Emoni Narawa in his way, and sound as he was in his tackle, he couldn't contain Savea with his full head of steam.
Wellington missed a critical chance just before halftime, and when the players returned, Trask landed a penalty goal after three minutes to reduce the margin to five points. Ten minutes later, he landed three more, but the vital break came in the 57th minute.
Bay of Plenty put together 24 phases of up-tempo, controlled pick and goes, but in the goalmouth, it was Narawa, in the dummy half, who picked up the ball and scored to claim the lead at 20-15.
Wellington finally managed an extended period of play in the Bay 22m area, and after a 16-phase build-up, they secured a penalty from which they opted for a scrum. Although untidy, they retained the ball and moved it wide, where Umaga-Jensen timed his pass perfectly to wing Losi Filipo who had the gap to get over for the equalising try.
A long restart resulted in Wellington touching the ball down and gaining a scrum feed back at halfway. A penalty was conceded, and Garden-Bachop attempted a 50m shot, but the kick went wide.
Regular time ended when Clarke looked to dive over in the corner, but the combination of Narawa's covering tackle and Clarke knocked the ball on. Bay of Plenty dropped out, and Garden-Bachop attended a dropped goal, but it was wide. Wellington then had a lineout feed in the 80th minute and mounted a 20-phase effort before Garden-Bachop knocked the ball on to end normal time tied.
Just before full-time, the Bay lost Narawa to an HIA.
Playing into the wind, the Bay camped in Wellington's half and ended with 27 phases but no score as they turned around.
Scorers: Wellington 23 (Julian Savea 2, Losi Filipo tries; Jackson Garden-Bachop con, pen; Callum Harkins pen) Bay of Plenty 20 (Aidan Ross, Emoni Narawa tries; Kaleb Trask 2 con, 2 pen). HT: 15-7. FT: 20-20