The 23-year-old fly-half was nigh-on flawless as he booted seven penalties and added the extras to tries from Phil Burleigh and Patrick Osborne to put the Dunedin side 35-12 ahead after 55 minutes.
Up until that point, the visitors had mustered just four penalties from Beauden Barrett, but prop Ben Franks narrowed the deficit with a converted try before they were given further hope when Jarrad Hoeata was sent to the sin bin.
The Hurricanes capitalised on their man advantage as Barrett touched down twice in the closing stages, but it proved to be in vain as they suffered their fourth defeat in their opening five Super XV matches.
A quiet first half gave no indication of the late drama that was to follow, with neither side crossing the line in the opening 40 minutes.
Sopoaga opened the scoring after seven minutes with a penalty although Barrett levelled almost immediately afterwards with his kick from 35 yards after Shane Christie had strayed offside.
The Hurricanes were then punished for their indiscipline at the breakdown as Sopoaga landed two penalties before adding another after Barrett had cut the gap to three points.
The pair then traded penalties before Sopoaga put the Highlanders 18-9 ahead at the break with his sixth effort at goal.
Barrett reduced the deficit with a penalty at the start of the second half before the hosts took charge in the 49th minute with the game's first try.
Aaron Smith was first denied by an excellent tackle by TJ Perenara, whose efforts were in vain as Ben and Aaron Smith combined to set up Burleigh, with Sopoaga tagging on the extras before adding a penalty soon after.
It appeared game over when Osborne intercepted Hadleigh Parkes' misplaced pass before sprinting clear to touch down and give the Highlanders a 35-12 lead with only 25 minutes left to play.
But their opponents refused to accept defeat and bossed possession to work their way into a decent position before a succession of penalties saw them get Franks over the line in the 62nd minute.
Their slim hopes were boosted six minutes later when Hoeata was given a yellow card before a breakaway finished with Perenara releasing Barrett to cross and the fly-half duly converted to cut the gap to nine points.
Barrett added another in the corner two minutes from time to take his points tally for the day to 26 and set up a tense finale, but the Highlanders hung on to claim victory.
- Sports & Recreation
- Beauden Barrett
- Patrick Osborne
- Phil Burleigh
- Ben Franks