Test centre Malakai Fekitoa's 18th-minute effort on the right edge was the only try in the four-point triumph, as both sides struggled in the Auckland wet.
Balls were dropped left, right and centre by both teams, while the Highlanders conceded 18 turnovers and the Blues gave up 23.
But the injury-ravaged Highlanders eventually ground out the win, relying on the kicking game of playmakers Lima Sopoaga and Aaron Smith to guide them home.
"It's just an awesome effort from the boys," skipper Elliot Dixon said.