The opening play saw the Steamers roar into the Otago 22 and the excellent set piece scrum led by prop Aidan Ross pushed Otago off the ball to win a penalty. Dan Hollinshead from a handy angle opened the scoring.
Otago won the kick-off back cleverly and swept onto attack but after turning the ball over, the Steamers gifted it back by trying to run the ball out with their trademark risk and reward policy.
It didn't work as the error was punished with a try to Thomas Franklin and conversion to Fletcher Smith for a 7-3 lead to Otago.
Strong driving play led by Steamers player of the year Joe Tupe showed a willingness to take Otago on up the middle of the park and after 19 minutes Hollinshead kicked another penalty to narrow the gap.
But Otago's ability to score from anywhere hurt the Steamers immediately, with flanker Naulia Dawai finishing off a fine move. Smith missed an easy penalty shot after 28 minutes to let the Steamers clear after concerted pressure.
Smith then spilled the ball and from the resulting scrum, centre Lalakai Foketi looked to score for the Steamers only for the try to be disallowed after a knock-on.
Trailing 14-6 at halftime the Steamers needed to get points on the board early in the second stanza boosted by All Blacks flanker Sam Cane on after the break.
But it was the home side who scored first through James Lentjes, as the Steamers simply ran out of defenders.
Trailing 21-6 the Steamers had to chase the game and with Cane prominent they surged forward winning a penalty.
From the lineout, Foketi surged across for his fourth try against Otago this season after a TMO review. Hollinshead closed the gap to 21-13 to give the Steamers hope.
Otago added three from the kicking tee after the assistant referee missed an Otago foot fault on the touchline that was decisive in the end.
Back came the Steamers but were penalised from a promising driving maul into the Otago 22. Franklin was yellow carded for an off the ball hit after 62 minutes that gave the Steamers an opportunity they were not able to use.
Cane, looking ring rusty after six weeks out with injury, spilt two passes in contact that ended promising moves.
Otago stretched their lead to 27-13 but Terence Hepetema scored a converted try with three minutes left to close to 27-20.
The Steamers surged out of their half and on the back of a penalty had one last chance to send it to extra time but a crucial turnover put an end to their season.
Otago 27 (Thomas Franklin, Naulia Dawai, James Lentjes tries; Fletcher Smith 3 cons, pen; Scott Eade pen) Bay of Plenty 20 (Lalakai Foketi, Terrence Hepetema tries; Dan Hollinshead con, 2 pens; Te Aihe Toma con) HT: 14-6