After starting positively with three wins from their opening five games, they went down 47-38 to the Cheetahs in Wellington last weekend in a match where they gave up a 21-point lead.
Tonight's win lifted them temporarily to fifth on the ladder, but that will change during this weekend's round of matches.
The Sharks, who began round seven in seventh place, beat the Brumbies 29-26 in Canberra last weekend.
Sharks coach John Plumtree elected to play Bismarck du Plessis from the bench after the dynamic Springboks hooker had played big minutes during the opening six rounds of the competition for the visitors and was also carrying a thigh injury.
Both sides burst in to life in the 31st minute when nearly every player on the paddock was involved in an on-field brawl.
Haymakers and upper-cuts flew in from all corners during a few frenetic seconds, while Hurricanes fullback Andre Taylor stood back and took in the view.
In the end, despite it being an old-fashioned dust-up, only Hurricanes flanker Karl Lowe and Sharks hooker Craig Burden were shown white cards, while Barrett added another three points for the home side, who were awarded a penalty.
Savea was called upon shortly after the scrap to finish a movement sparked by Taylor and the big wing made no mistake as he finished in the left-hand corner to bag his first Super Rugby try in his 17th appearance for the Hurricanes.
Earlier, Taylor had opened the scoring when he cut through the Sharks backline from a Bateman pass, while Lam crashed over from close-range midway through the first half.
The match marked the 11th time the Hurricanes have played in New Plymouth and their latest encounter was against the Cheetahs in 2009, which they won 29-12.
The win left the Hurricanes in a good state ahead of their bye week, with four wins from seven.
Their next game is on April 21 when they host the Crusaders at Westpac Stadium. The Sharks now travel to Auckland to meet the one-win five-loss Blues at Eden Park next Friday night.
Hurricanes 42 (Andre Taylor, Jack Lam, Julian Savea, Conrad Smith, Tim Bateman, Jeremy Thrush tries; Beauden Barrett 3 cons, 2 pens) Sharks 18 (JP Pietersen, Craig Burden tries; Frederic Michalak 2 pens, con) HT: 25-3APNZ