The South African side scored the only try of the match, a penalty try off a scrum in the 10th minute, but spent large chunks of the game defending their own line.
Even after the final siren sounded, the Stormers were under pressure, with the Force denied a last-gasp try when fullback Dane Haylett-Petty was ruled to have been held up over the line.
“It wasn't pretty but we'll take the four points,” said the Stormers captain Juan de Jongh.
Stormers moved to the top of the South African conference, although the Bulls can leapfrog them if they win later on Saturday.
The Force remained second from bottom after the Australians suffered their eighth successive loss of the season.
“It was the same story,” Force captain Ben McCalman said. “We worked hard, we put ourselves in position to score but we couldn't capitalise.”
Original source: Stormers edge Force in Super rugby