Laumape's second try was the result of an audacious chip-pass from All Blacks flyhalf Beauden Barrett about 15 metres out from his own line and with flanker Brad Shields in the sinbin as the home side weathered a relentless Stormers attack.
Fullback Jordie Barrett also crossed twice, while Julian Savea, Cory Jane and Beauden Barrett grabbed tries for the home side.
Stormers' replacement hooker Ramone Samuels scored the visitors only try with fullback SP Marais slotting four penalties, while flyhalf Robert du Preez kicked a penalty and conversion before he went off injured.
The Stormers had suffered heavy defeats to the Canterbury Crusaders and Otago Highlanders over the last two weeks but limited their game to a battle among the forwards on Friday.
Captain Siya Kolisi drove his side over the advantage line, marshalled their fringe defence and upset the quick ball the Hurricanes thrive on.
All four of the Hurricanes first half tries came from well-placed kicks with Beauden Barrett providing three chip-passes out to the flanks where Jane, his brother Jordie and Savea all scored.
Jordie Barrett's first try also came from a grubber kick by scrumhalf TJ Perenara, however the fullback had to strip the ball from Stormers number eight Nizaam Carr and force it just before the deadball line.
The South Africans refused to let the home side get too far in front with replacement hooker Samuels, on for the sinbinned Mbongeni Mbonambi, crashing over from an attacking lineout drive.
They further capitalised on some poor discipline from the home side late in the first half when Marais took over goalkicking duties from the injured du Preez and slotted two penalties to reduce the gap to 22-16 at the break.
The Stormers built on their momentum after the interval with Marais kicking two more long-range penalties to level the score.
Laumape then smashed his way over after the Hurricanes scrum had destroyed the Stormers in the midfield and Perenara took a quick penalty to give them some fast ball and field position.
With Shields in the sinbin for deliberately collapsing a rolling maul, the Stormers were in with a chance of snatching a morale boosting win while trailing 27-22 and hot on attack.
The Hurricanes, however, turned the ball over and Barrett again kicked wide to set up Laumape's second try.
Photo: Photosport Ngani Laumape celebrates his try.