The visitors enjoyed 68 per cent of the possession during the first 11 minutes. Former Otago halfback Brad Weber scored the Magpies second try in the 12th minute after superb buildup work from Taulagi and winger Mason Emerson.
Taulagi again slotted the extras. The only poor aspect of the Magpies' play during the first quarter was two poor lineout throws from hooker Kianu Kereru-Symes who again impressed with his defensive workrate.
Otago, the second qualifiers and Ranfurly Shield holders, opened their account with a 26th minute penalty to first five-eighth Josh Ioane when Magpies flanker Geoff Cridge was offside.
The Magpies produced some outstanding defence late in the first half when Otago retained possession for 14 phases before Magpies co-captain and openside flanker Gareth Evans, another former Otago player, forced a turnover. The visitors led 14-3 at halftime.
Hawke's Bay had 46 per cent of the territory and 43 per cent of the possession in the first half.
Otago introduced experienced loosie James Lentjes and All Blacks hooker Liam Coltman off the subs bench at halftime and it was Lentjes who made an immediate impact, forcing an early turnover.
Fortunately for the Magpies they were quick to win the ball back. However Otago were first to score in the second half when winger Mitchell Scott dashed over in the 49th minute after clever play earlier on from centre Matt Faddes. Ioane converted from out wide.
Magpies winger Jonah Lowe was unlucky to be forced into touch by Otago fullback and captain Michael Collins in a tryscoring situation in the 53rd minute after a spectacular solo run from first five-eighth Lincoln McClutchie.
Emerson put the Magpies ahead 19-10 with his 62nd minute try after clever buildup work from centre Stacey Ili. Otago remained in the hunt when second five-eighth Sio Tomkinson scored in the 72nd minute and Ioane converted.
After Ioane missed a penalty attempt from 45 metres out in the 77th minute he had his moment of glory seconds after the final siren.
Otago could end the 2018 season with the Log o Wood and promotion to the Premiership should they beat Waikato in Friday night's final in Hamilton.
"That's the worst way to go. We lost our way with seven minutes to go. We tried to close it up rather than keep playing," co-captain Weber said afterwards.
"We felt good at halftime and the confidence was there. Just a couple of lapses cost us."
"While we're gutted we could not go to the big dance we've got so many young fellahs who have stepped up this season. For years to come it will be outstanding moving forward," Weber added.
Match highlights
Heartstopper: Magpies prop Ben May's dropped ball in the 35th minute when the visitors were hot on attack. A crucial error during a powerful performance from May who returned after missing the previous game with a hamstring injury.
Turning point: When Otago first five-eighth Josh Ioane kicked the matchwinning penalty in the 81st minute.
Player of the match: Otago lock Josh Dickson. A phenomenal workrate and inspirational throughout for the hosts.
Scorers: Hawke's Bay Magpies 19 (Marino Mikaele-Tu'u, Brad Weber, Mason Emerson tries; JJ Taulagi 2 cons ), Otago 20 (Mitchell Scott, Sio Tomkinson tries; Josh Ioane 2pens, 2 cons ). HT: 14-3.
