The victory moved Southland to second place in the Championship - for now - and they look odds on to finish in the top four with games to come against Hawkes Bay and Counties Manukau.
The Stags scored five tries in all as Willis Halaholo, Cardiff Vaega, Elliot Dixon, Scott Eade and Tayler Adams all got on the scoresheet, while a collection of penalties and conversions from Eade proved useful.
The turning point came after Marty McKenzie left the field with an injury and Scott Eade moved to pivot.
Eade began the game at halfback but with him running the cutter and replacement No 9 Adams on the paddock, Southland enjoyed better direction in the second half of a game that lacked structure as it was played at such a frenetic pace.
The contest was a great advertisement for indoor stadiums as both sides were able to throw the ball around without having to navigate the conditions.
Otago wing Buxton Popoali'i had a blinder as he bagged a double, including the game's first five-pointer, and he also made a brilliant try-saving tackle late in the piece.
Hayden Parker's goalkicking kept Otago in the contest, while he also added a crucial try late in the first spell on the back of a chip-kick gone wrong from Southland fullback Robbie Robinson.
With a 20-11 lead at the break Otago looked like they would kick on to a win in front of their home fans but the Stags never gave in and were duly rewarded when the final whistle blew as their comeback was complete.
Cardiac Stags: Southland have now chalked up three come-from-behind wins in a row as their season has been given a much-needed dose of adrenalin. They will be a handful come playoff time
Try of the match: Southland's midfield of Willis Halaholo and Cardiff Vaega are pairing loaded with bombast and they were part of a brilliant breakout try in the first spell that was finished off by Halaholo. It was scintillating stuff.
Southland 38 (Willis Halaholo, Cardiff Vaega, Elliot Dixon, Scott Eade, Tayler Adams tries; Marty McKenzie pen, Eade 2 pen, 2 con)
Otago 32 (Buxton Popoali'i 2, Hayden Parker, Kieran Moffat tries; Parker 2 pen, 3 con)
HT: 11-20