The home side trailed 17-0 at the break but played better in the second half and got back to 17-10 with a quarter of the game gone.
But it coughed up the ball at vital times and found it hard to get through a committed Bay of Plenty defence.
Spirit coach Kane Jury said the first-half ill-discipline was costly in the end.
"In that first half we put ourselves under pressure all the time. We gave away penalties and we can control that," he said.
"We were offside a lot of the time and that caused us to go down to 14 players. That allowed them to break out.
"They’ve got a lot of speed out wide so against a disorganised defence like ours was because of the lack of numbers that was always going to be hard."
Jury said the side came back into the game in the second half and he praised the side’s set piece which had been struggling in previous games.
The team had opportunities in the second half but just went too far with the ball when it needed to be pushed.
Otago winger Sam Hollows was yellow carded for persistent offside after 28 minutes and, as soon as she finished her 10 minutes off the park, Spirit prop Syreeta Norris went to the naughty chair for again being offside.
It did not help the Spirit cause and, with captain Angie Sisifa struggling with knee and ankle knocks, the side did well to hang in the game.
Bay of Plenty centre Aryahn Clarke helped herself to two tries in the first half .
Otago lock Julia Gorinski scored the first try for Otago, three minutes into the second half.
But Bay of Plenty skipped clear with another couple of tries before replacement forward Annemileke van Vielt scored at the end of Otago.
Best for Otago were flanker Georgia Mason and midfield back Kilistina Moata’ane.
Bay of Plenty will host the Championship final and has the next two weeks off. Otago will take on North Harbour next week in Auckland in the semifinal between the second and third-placed teams in the Championship which will go on to play Bay of Plenty.
Farah Palmer Cup
The scores
Bay of Plenty 27
Ora Williams 2, Aryahn Clarke 2, Ereti Williams tries; Crystal Mayes con
Otago 17
Julia Gorinski, Annemieke van Vliet tries; Liv Waldron 2 con, pen
Halftime: 17-0