The victory ensured the Hurricanes retained their unbeaten season with their fifth win and moved them to the top of the table on 22 points, two ahead of Australia's Brumbies.
The Hurricanes dominated possession and territory but kept on dropping the ball or being penalised at the ruck and were held up over the line several times by a tenacious Highlanders' defence.
The Dunedin-based side came alive with around 15 minutes remaining and launched wave after wave of attack only to be thwarted themselves.
A crunching tackle from inside centre Ma'a Nonu on All Blacks team mate Malakai Fekitoa, his third in about five minutes, created the turnover that led to the Hurricanes sweeping down field for Perenara's try.
The only scoring in the first spell was a penalty apiece to flyhalves Lima Sopoaga and Beauden Barrett, who both also missed a shot at goal.
Hurricanes loosehead prop Reggie Goodes barrelled over for a second half try, which was converted by Barrett, who also added another penalty but missed another easily kickable shot.
Sopoaga scored a try with about two minutes remaining after Julian Savea had been yellow-carded for a professional foul and then turned possession over following a questionable call from referee Ben O'Keefe that a long pass had gone forward.
