Jordie Barrett, who ended the game at second five in place of Laumape, set up the latter's first try with a pinpoint crosskick and then gave an exquisite flick miss pass behind his back to a grateful Matt Proctor.
The Hurricanes were even able to cope with the sinbinning of TJ Perenara for a careless high tackle on Highlanders' No 10 Fletcher Smith.
Wing Vince Aso scored his third double in four games, and again looked the goods, if slightly out of position.
The first spell was tight, intense and absorbing, but devoid of the spite that pockmarked the Hurricanes' clash with the Chiefs last weekend.
That is was only 10-8 can be attributed to the fact that the Highlanders forwards rolled their sleeves up and hacked into their work, while their backs, using an umbrella rush defence - from the outside in - were accurate and bruising on the tackle. The likes of Tom Franklin and Liam Coltman were industrious.
The Hurricanes were a touch too excitable early, spreading the ball at will, yet not necessarily doing the yards up the middle. But they were physical and threatening, and lock Michael Fatialofa was the go-to man at lineout time. However, the first try went to No 8 Ardie Savea, jumping in the middle of the lineout before latching into the back of the maul before ploughing over. He was his usual dynamic, ubiquitous self.
One of the key moments of that first stanza came when Highlanders centre Malakai Fekitoa left for a concussion test, and never returned. He had been hurt after a Jordie Barrett tackle, which came under closer inspection but was ruled fair by referee Angus Gardner. In one fell swoop, that removed some of the Highlanders' starch on defence and punch on attack.
Ben Smith looked to have erred when he opted for a scrum from a penalty almost in front of the Hurricanes' posts, but another solid visiting scrum and a sweet Aaron Smith pass saw replacement Matt Faddes cross.
The Hurricanes' riposte was swift, Jordie Barrett setting up Laumape with that crosskick.
The Highlanders knew only brief joy in the second spell, Elliot Dixon diving over from quick Aaron Smith ball. Tevita Li capped an unhappy night with a yellow card for a no-arms tackle.
The Hurricanes have the bye next weekend, while the Highlanders travel to Canberra to face the Brumbies, their first non-New Zealand Conference clash. They will welcome the respite.
Hurricanes 41 (N. Laumape 2, V. Aso 2, A. Savea, M. Proctor, J. Savea tries; B. Barrett 2 cons, J. Barrett con) Highlanders 15 (M. Faddes, E. Dixon tries; M. Banks con; F. Smith pen) HT: 10-8
Match stats