Trailing 5-8 at halftime the Highlanders, on the back of a powerful performance from their loose forward trio of blindside flanker Thompson, No 8 George Naoupu and openside flanker Alando Soakai, scored 27 unanswered points in the second half for their second win of the season.
The Cheetahs return home with their record of not having beaten a New Zealand team away since the inception of Super rugby, intact.
They also lost to the Hurricanes and the Blues in the previous two weeks and now head home to lick their wounds on their bye round before hosting the Brumbies in two weeks.
Today's fine win pushes the Highlanders, who started the match third from the bottom to midfield in the table on 13 points from six matches.
Today's fine all-round team performance and their pack's dominance over the Cheetahs will give the Highlanders confidence as the eye the Bulls for their next match at Palmerston North.
The Highlanders, with skipper Jimmy Cowan working the ball well from the base of rucks and scrums, had the Cheetahs back-pedalling from the start of the match but a couple of lapses saw them trailing at halftime.
Thompson got his first try, finishing off a controlled drive from a five-metre lineout to give his side the lead after the Cheetahs led with an early penalty.
But the Cheetahs took the lead again when Cowan failed to field a high kick cleanly, giving centre Corne Uys the chance to break the defence for an unconverted try.
A 15-point burst inside 18 minutes of the resumption saw the Highlanders take a stranglehold on the free-flowing game.
Dagg scored his first try following up a grubber into the corner by first five-eighth Mathew Berquist who then knocked over a penalty. Then, Steven Setephano, filling in for Soakai who was in the blood bin, finished off a thundering break down the centre by Naoupu to score by the right post.
The Cheetahs came back to test the Highlanders' defence midway through the half but were turned back each time before bombing their best chance with a forward pass.
The Highlanders, coming off a 10-14 loss to the Chiefs last week, regained territorial advantage and Thompson and Dagg found gaps in a tiring Cheetahs defence to score their second tries of the match.
