It was the 13th win in 15 matches for the Stormers -- but the Western Cape team gave a stumbling performance and maintained a dubious record of failing to secure a bonus point for scoring four tries in any of their games.
They will go into the final round of league matches one point on the overall log behind New Zealand's Waikato Chiefs. If they had secured a bonus point they would have taken top spot because of having more wins.
"They were terrible conditions," said Stormers captain Jean de Villiers. "We couldn't play too much rugby. We were actually better off not having the ball.
"We got the win. It would have been nice to have got the bonus point but we'll take the four points."
Chiefs are away to the Hurricanes in Wellington next Friday, while the Stormers host the struggling Melbourne Rebels in Cape Town a day later.
Another win will secure a home semi-final for Stormers -- and they could still finish top of the log, with a potential home final, if the Chiefs slip up.
The slippery conditions made running rugby difficult for both teams, but Stormers let several try-scoring opportunities get away by holding on to the ball too long or kicking possession away.
The only try came in the 54th minute when right wing Gio Aplon ran on to a perfectly-judged chip from fly-half Peter Grant while Cheetahs full-back Willie le Roux was in the 'sin bin'.
Grant added the conversion and also kicked two penalty goals.
Cheetahs fly-half Riaan Smit landed two penalties for the home team. The teams were level at 3-3 at half-time.
With rain falling for much of the game, both teams opted to put pressure on their opponents with high kicks. Neither team was willing to run the ball the contest was largely between the forwards.
Although Stormers often got good possession, they were thwarted by solid Cheetahs' defending.
Flank Heinrich Brussow, who was not called up by new Springbok coach Heyneke Meyer for the recent series against England, was in his element, burrowing into the mauls and stealing the ball from Stormers on numerous occasions.