Ahead 15-9 at the break, the Highlanders were in front for all but the first four minutes of the match, though at one stage it looked like it was going to be the familiar and depressing story of being on the wrong end of a close scoreline.
The Cheetahs got within two points midway through the second half after a debatable Heinrich Brussouw try but the visiting side managed to stay composed in the final stages to grab its first win of the season.
The match was sealed by the Highlanders with eight minutes left in the match.
Highlanders first five-eighth Michael Hobbs broke through the Cheetahs defence and fed Jason Shoemark.
When Shoemark was held up just half a metre short, Hobbs was on hand to burrow over beside the posts to give the Highlanders, with Israel Dagg's conversion, a 12 point lead.
It was Hobbs' fourth try in three games and secured the victory, although the fingernails were in work for Highlanders fans with three minutes to go after Cheetahs captain Juan Smith barged over.
But the Cheetahs mucked up the kick-off and the Highlanders nearly scored a bonus point try right at the end, but Adam Thomson was ruled to have grounded the ball short of the tryline.
It was a match where neither team could get any foothold and ball was spilt or an error occurred at a key moment.
The Cheetahs had their chances but were not ruthless enough and lacked a playmaker at key times.
The Highlanders' backs looked lively when they had the ball for periods but too often failed to string enough phases together.
The Highlanders' lineout was reasonably solid but the scrums were messy throughout.
Thomson had a good game for the Highlanders while openside flanker Alando Soakai got through plenty of work.
Jamie Mackintosh got round the paddock for the visitors.
Kendrick Lynn showed some good touches in his first game at centre for the Highlanders while Fetu'u Vainikolo ran hard when he had the ball.
Dagg again showed his class at the back.
The Highlanders scored the first try of the game, after just seven minutes.
Moving the ball through a few phases that man Hobbs then managed to get in behind the defence, and fed a charging Jason Rutledge.
From the resulting ruck, prop Clint Newland passed to a flying Lynn who strolled over behind the posts.
Naas Olivier had earlier slotted a penalty for the home side and he repeated the effort halfway through the first half.
But the Highlanders went further ahead after a turnover saw Vainikolo scamper 70m to score.
Cheetahs hooker Adriaan Strauss coughed up the pill after a good tackle by Thomson and Lynn and Vainikolo was untouched as he sprinted away.
Hobbs missed the easy conversion.
After Olivier had kicked over a third penalty, Dagg replied for the Highlanders, putting one over from straight in front and 35m out in the final act of the first period.
Best for the home side was midfield back Meyer Bosman and Brussouw, who made a storming 20m run to score his try.
But it was questionable whether it should have been awarded after it looked like the ball had been held up over the line.
