Hurricanes first five Barrett was at his mercurial best as he set up the opening try.
After regathering his own chip-kick, the All Black ran cross-field around the defence, before off-loading on the 5m line to the try-scorer, Willis Halaholo.
Barrett scored the second try himself after intercepting a pass on halfway and sprinting under the cross-bar.
With a 15-6 half-time lead, the Hurricanes extended their advantage in the second half when Victor Vito broke from the base of a scrum to crash over the line.
The Chiefs dominated the set piece for a majority of the contest as the Hurricanes played without influential captain Dane Coles, but explosive line speed and a ferocious defence kept the home side in the match.
They also took whatever scoring opportunities that came their way with Barrett also kicking two conversions and two penalties for a personal tally of 15 points.
Chiefs fullback Damian McKenzie slotted three penalties for the visitors, who were unable to capitalise on numerous try-scoring opportunities.
The Hurricanes, who had been heavily penalised by referee Angus Gardner, also spent 10 second-half minutes reduced to 14 men after winger Cory Jane was yellow-carded for a deliberate knock down.
Neither side were really able to stamp their authority on the contest in the first quarter until McKenzie put the Chiefs on the board with a penalty soon after Halaholo's try and the hosts were then placed under siege in their own 22m area.
A try-saving tackle by captain TJ Perenara on McKenzie, however, relieved the pressure and the home side jumped to a 15-3 lead on Barrett's first penalty and his intercept try.
A McKenzie penalty reduced the deficit to 15-6 at the break, before Cane was penalised after he ran into Hurricanes hooker Ricky Riccitelli for no reason inside the home side's territory, which set up the field position for Vito's try.
McKenzie and Barrett then traded penalties but the Chiefs were unable to capitalise on the man advantage nor break through the yellow and black wall that blocked their path to the try line.
The Hurricanes haven't conceded a try in their last 341 minutes on the field.
They'll host the Lions in next weekend's final, after the South Africans ended the Highlanders' championship defence with a 42-30 victory in the second semi-final in Johannesburg.
Baeuden Barrett makes a break. Photo: PHOTOSPORT