The three tries to two win was a gutsy effort from the home side, but the visiting Highlanders now sit winless after three games.
The Hurricanes were strong on defence in Wellington and their bench players made an impact when they came on the field.
Both teams made plenty of errors, but the Hurricanes endured for their second straight win, after last week beating the Blues in a stunning finish.
Hurricanes captain Ardie Savea said Covid-19 was going through the team.
"With omicron, there were some late changes," Savea said.