A tired second-half display allowed the 12th-placed Stormers to steal the first victory of their arduous Australasian tour in a deserved two tries-to-one display.
Their second straight loss left the Highlanders contemplating another mid to lower table finish to the season, with three matches on the road remaining.
They looked like keeping their playoff hopes alive after leading 6-0 at halftime but ultimately succumbed to a visiting side who played with more physicality, a superior kicking game and a desperation to notch their first win at Carisbrook.
The scores were locked at 11-11 before second five-eighth Peter Grant crossed out wide with 10 minutes remaining to reward the visitors for their edge in possession and territory through the second spell.
Lacking the fire up front that marked the middle part of their campaign, the Highlanders struggled for quality front foot ball to give space to the likes of gifted fullback Israel Dagg.
The Stormers relied on the boot of first five-eighth Willem de Waal for territory as their reconfigured backline largely struggled without the direction of injured captain Jean de Villiers.
They were powerful in the pack, especially at scrum time and the breakdown, although captain Schalk Burger struggled there to come to grips with the authoritarian refereeing style of Australian Matt Goddard.
Grant missed a penalty and his team trailed 6-0 at the end of a dour first half, courtesy of penalties in the 23rd and 32nd minute to first five-eighth Mathew Berquist.
In the 10 minutes after halftime, the Stormers scrored a try to winger Sireli Naqelevuki _ a 50m gift following a messy Highlanders grubber kick _ and penalty to de Waal.
Dagg helped his side regain the lead with a classic sidestep and acceleration from just inside his own half to break clear before putting winger Ben Smith over in the corner.
It was another brilliant moment in what has been has been an outstanding debut Super rugby season for the Hawke's Bay custodian.
However, the Stormers wouldn't lie down, levelling through a de Waal penalty before Grant's late heroics.
The Highlanders begin a South African excursion against the Sharks next weekend while the Stormers are at home to the Chiefs.
Results: Stormers 18 (Sireli Naqelevuki, Peter Grant tries; Willem de Waal 2 pen, con) Highlanders 11 (Ben Smith try; Mathew Berquist 2 pen). Halftime: 0-6.
