Four penalties from fly-half Riaan Smit and a late breakaway try from winger Willie le Roux proved enough to add a third win to the more impressive road victories over the Otago Highlanders and New South Wales Waratahs.
The Force, who also came into the match on a high after upsetting the Queensland Reds last week, enjoyed the majority of possession but had only Winston Stanley's converted first-half try and one Jayden Hayward penalty to show for it.
"It's important when you are not at your best to still win and we were a bit lucky but we'll take it," Cheetahs skipper Adrian Strauss said.
"We want to win every game but we'll take the three on the tour and hopefully we can keep up the momentum back home."
Both sides showed plenty of attacking intent but the frequent errors made the match a poor advertisement for southern hemisphere rugby.
The first score of the match came after 25 minutes when Cheetahs fly-half Smit kicked the first of his two penalties in the half but three minutes later the hosts raised the stakes.
The Cheetahs were trying to play the ball out of their own 22 when the Force won a turnover and quick hands allowed centre Stanley to touch down in the corner for the game's first try.
The Force should have had a second try just before half time after an electric break up the middle from centre Kyle Godwin but Wallabies prop Pek Cowan knocked on in contact close to the line.
The Force held their 7-6 halftime lead until the hour mark when Hayward, a second-half replacement for the injured Sias Ebersohn, slotted his penalty to extend it.
Seven minutes later and it was the Cheetahs' turn to blow a try-scoring opportunity, number eight Philip van der Walt knocking on as he tried to force the ball over the line.
Smit added his third and fourth penalties in the space of three minutes to put the visitors back in front, however, and, with the 80 minutes all but up, Le Roux was quickest to react to Robert Ebersohn's hack and raced away to score.
"Obviously a disappointing performance," said Force skipper Cowan, whose team were making their home debut after playing their first four matches of the season on the road.
"We just didn't deliver tonight, we didn't capitalise and we didn't put points on the board."
- Sports & Recreation